Map from Google - Norway

Norway is a Nordic country, but it is influenced by the warming influence of the Gulf Stream, so its climate is less cold than you might think, particularly along the west coast. However, the country is very extended in latitude, with a rugged coastline, plateaus and mountain ranges, so it has different climates to be taken into account.
The ocean (whose surface temperature reamins a few degrees above freezing even in winter) temper the winter weather, while it remains cool in the summer, therefore reducing the annual temperature range along the coast. This mild influence hardly affects the interior, because in Norway there are almost no plains, hence, highlands and mountain ranges block or at least hinder the penetration of mild currents coming from the sea.
The following map shows the climate zones of Norway.

Norway climate zones

The west coast has a cool, wet climate, characterized by the frequent passage of weather fronts, so that clouds, rain and wind dominate throughout the year.
During winter, the temperature remains slightly above freezing (0 °C or 32 °F) in the southern part, so that Bergen, the second largest city in the country, has an average temperature in January and February around 2 °C (35.5 °F). Precipitation does not always occur in the form of snow, but often in the form of continuous and cold drizzle.
Here are the average temperatures of Bergen.
Average temperatures - Bergen
BergenJanFebMarAprMayJunJulAugSepOctNovDec
BergenJFMAMJJASOND
Min (°C)0-11371012129731
Max (°C)446914171817141175
Min (°F)323034374550545448453734
Max (°F)393943485763646357524541

The temperature of the sea at Bergen is cold, but it's mild for the latitude, as we can see from the following table.
Sea temperature - Bergen
BergenJanFebMarAprMayJunJulAugSepOctNovDec
BergenJFMAMJJASOND
Sea (°C)76668111415131198
Sea (°F)454343434652575955524846

Moving to the north, the temperature gradually decreases, but the average daily temperature reaches the freezing point only around the 65th parallel, just below the Arctic Circle. It's remarkable that the Lofoten and Vesteralen Islands, located above the Arctic Circle itself, even in winter can sometimes experience rain instead of snow. Continuing to the north, the temperature goes down a few degrees below freezing, and the snow becomes frequent even along the coast, but at this point we enter in the climate area of the northern coast (as shown in the map above).
The sea, which in winter makes the air milder, during summer becomes a source of cool air, so that in July and August, along the west coast the maximum temperatures are around 15 °C (59 °F), and the minima around 10 °C (50 °F). However, if you move a few kilometres (or miles) inland, you can experience an increase in daytime temperatures, which can rise by a few degrees, and this happens in Bergen and other towns located not directly on the ocean coast, but within fjords.
The rainfall is quite common along the western slope. In the southern area, it's also abundant: in Bergen the average annual precipitation is about 2,200 millimetres (87 inches), but in cities located at the foot of the hills it can exceed 3,000 mm (118 in).
Here is the average precipitation in Bergen.
Average precipitation - Bergen
BergenJanFebMarAprMayJunJulAugSepOctNovDecYear
BergenJFMAMJJASONDY
Prec. (mm)1901501701151051301501902852702602352250
Prec.(in)7.55.96.74.54.15.15.97.511.210.610.29.388.6
Days211719171716181923242222235

Continuing to the north along the coast, rainfall is still frequent, but it becomes less abundant, and drops below 1,000 mm (40 in) in the coast north of Trondheim, although it can still reach 2,000 mm (79 in) in the slopes near the coast, where there are hills directly exposed to the westerly winds.

The north coast is a bit colder than the western one, and has a subpolar oceanic climate, although a branch of the Gulf Stream arrives here as well. The result is that the open sea does not freeze even at these latitudes, and this is a unique fact in the world. The following table shows the temperature of the sea at the North Cape.
Sea temperature - North Cape
North CapeJanFebMarAprMayJunJulAugSepOctNovDec
North CapeJFMAMJJASOND
Sea (°C)5444579109766
Sea (°F)413939394145485048454343

The average winter temperatures, however, drop below freezing, and tend to decrease moving towards the east: the average in January and February ranges from -2 °C to -6 °C (28 to 21 °F), from the west to the east. At North Cape, in winter the temperatures are similar to those of Oslo, even though here the winter lasts longer. The northern coast is close enough to the Pole and thus is subject to the polar winds, which can be furious, especially in winter and spring.
Average temperatures - North Cape
North CapeJanFebMarAprMayJunJulAugSepOctNovDec
North CapeJFMAMJJASOND
Min (°C)-6-6-4-2258852-2-4
Max (°C)-2-2-11591312951-1
Min (°F)212125283641464641362825
Max (°F)282830344148555448413430

In summer, July and August, which have an average temperature around 10 °C (50 °F), are the mildest and also the quietest months, with the lowest risk of wind. Near the Arctic Circle, you can see the midnight sun around the summer solstice (21 June), and for a period much longer as you head north. At the North Cape, the sun never sets from mid-May to late July.
At North Cape, precipitation amounts to about 800 mm (31.5 in) per year. Summer is the least rainy season, although there are still 9/10 days with rain per month. Here is the average precipitation.
Average precipitation - North Cape
North CapeJanFebMarAprMayJunJulAugSepOctNovDecYear
North CapeJFMAMJJASONDY
Prec. (mm)9575656040404550608580100795
Prec.(in)3.732.62.41.61.61.822.43.33.13.931.3
Days18151514111091014181719170

Even here on the north coast, within the fjords there's a decrease in the winter temperatures, so that in the deepest fjord the sea can freeze in winter, and an increase in the summer temperatures: in fact here the effect is even more pronounced than on the west coast. For example, in Lakselv, located in the southern part of a fjord, more than 120 kilometres (75 miles) away from the ocean coast, the average in January is -10 °C (14 °F), while directly on the coast it's just -4 °C (25 °F).

The south coast, facing south-east, on the Skagerrak strait which separates Norway from Denmark, is less influenced by the ocean than the west coast, therefore it is less humid and rainy compared with the area of Bergen, a little colder in winter (with average temperatures just below freezing), and warmer in summer, with a daily maximum around 20 °C (68 °F), when the stay is pleasant and you can expect even some sunshine.
Average temperatures - Kristiansand
KristiansandJanFebMarAprMayJunJulAugSepOctNovDec
KristiansandJFMAMJJASOND
Min (°C)-5-5-21691110850-3
Max (°C)124914192019161163
Min (°F)232328344348525046413227
Max (°F)343639485766686661524337

In Kristiansand, precipitation amounts to 1,300 mm (51 in) per year, so it is quite abundant, but it's still much better than in Bergen.
Average precipitation - Kristiansand
KristiansandJanFebMarAprMayJunJulAugSepOctNovDecYear
KristiansandJFMAMJJASONDY
Prec. (mm)1208085608575901201401651651151300
Prec.(in)4.73.13.32.43.333.54.75.56.56.54.551.2
Days191516121412131718192019194

The fjords of Norway, which we have already mentioned, have different microclimates depending on their shape and size, and also on slope exposure, but generally, the more they penetrate inland, the less they become rainy throughout the year, while they become colder in winter and warmer and sunnier in summer. For example, the city of Trondheim, located inside a large and deep fjord extended into the western coast, has an average temperature of -3.5 °C (25.5 °F) in January, and an average of 14 °C (57 °F) in July, and therefore it can be included in the continental climate zone, while in Kristiansund, on the west coast at the same latitude, the average is 1 °C (34 °F) in January, and 13 °C (55.5 °F) in July.
Average temperatures - Trondheim
TrondheimJanFebMarAprMayJunJulAugSepOctNovDec
TrondheimJFMAMJJASOND
Min (°C)-7-6-3059101073-2-5
Max (°C)01481417181814942
Min (°F)192127324148505045372823
Max (°F)323439465763646457483936

In Trondheim, about 900 mm (35.5 in) of rain or snow per year fall; here also the wettest season is autumn. Here is average precipitation.
Average precipitation - Trondheim
TrondheimJanFebMarAprMayJunJulAugSepOctNovDecYear
TrondheimJFMAMJJASONDY
Prec. (mm)65505550557095851151057085890
Prec.(in)2.622.222.22.83.73.34.54.12.83.335
Days181616161517191822221819216

The inland areas of Norway have a continental climate, with cold, snowy winters and mild summers. Typically the interior is covered with hills and mountains, and the temperature decreases with increasing altitude, so that at higher altitudes there is a mountain climate. The snowline in Norway is quite low, about 1,500 metres (4,900 feet).
The coldest area of the country is the Norwegian part of Lapland, which corresponds to the southern part of the Finnmark County. Here the winter is really frigid, in fact the temperature can drop to -50 °C (-58 °F) in the worst moments. Summer is short but intense: in the three months, during which the temperature rises above freezing even at night, the vegetation explodes, and the days are very long. Sometimes it can get even hot, so that the daytime temperature can reach 30 °C (86 °F), while the nigths remain cool or even cold.
Average temperatures - Karasjok
KarasjokJanFebMarAprMayJunJulAugSepOctNovDec
KarasjokJFMAMJJASOND
Min (°C)-23-22-17-9-15862-5-14-21
Max (°C)-12-10-41715181592-5-10
Min (°F)-9-81163041464336237-6
Max (°F)101425344559645948362314

In this area, precipitation is much scarcer than in the rest of Norway, both for the distance from the sea and for the cold, so that it does not reach 400 mm (16 in) per year, although in summer, when temperatures rise, precipitation, which in this season occurs in the form of rain, is more abundant. Here is average precipitation in Karasjok.
Average precipitation - Karasjok
KarasjokJanFebMarAprMayJunJulAugSepOctNovDecYear
KarasjokJFMAMJJASONDY
Prec. (mm)201515152540706040352015365
Prec.(in)0.80.60.60.611.62.82.41.61.40.80.614.4
Days6555681111987687

In the central area, on the border with Sweden, ie the northern part of Hedmark and the eastern part of Sør-Trøndelag, very marked continental features are also found because of the distance from the sea, of its belonging to the eastern slope, and of altitude, as this area is dominated by a high plateau between 500 and 1,000 metres (1,600 and 3,300 feet). Here during the winter, the temperature can drop below -40 °C (-40 °F).

Sognefjord

The area of Oslo, along the south-eastern part of Norway, has a Baltic (slightly continental) climate: winters are cold, with temperatures a few degrees below freezing in the winter months, and frequent snowfall. During winter, mild air masses from the Atlantic ocean can sometimes penetrate even here, so that rain may fall instead of snow, while on other occasions, cold spells are possible, due to air masses from Russia, which may lower the temperature to -25 °C (-13 °F). The average temperature hovers around freezing in November and March, and is mild in the three summer months (June, July and August), with a maximum around 20/22 °C (68/72 °F). Rainfall is moderate, but well distributed throughout the year, with a maximum between summer and autumn, and a minimum in spring. Like other cities of the country, Oslo is located in a fjord, more than 80 kilometres (50 miles) deep.
Average temperatures - Oslo
OsloJanFebMarAprMayJunJulAugSepOctNovDec
OsloJFMAMJJASOND
Min (°C)-7-7-31711121184-2-6
Max (°C)-2-149162022201593-1
Min (°F)191927344552545246392821
Max (°F)283039486168726859483730

The sea temperature in the Oslo fjord reaches 17 °C (63 °F) in July and August.
Sea temperature - Oslo
OsloJanFebMarAprMayJunJulAugSepOctNovDec
OsloJFMAMJJASOND
Sea (°C)544610141717151296
Sea (°F)413939435057636359544843

Finally, there are the northern islands.

The island of Jan Mayen, situated between the Atlantic Ocean and the Arctic Ocean, has a subarctic climate.

Further to the north, we find Svalbard, the northernmost part of Norway, which is colder in winter.

When to go

The best time to go to Norway is the summer, from June to August. The temperatures are very cool along the coast and in mountainous areas, and even cold along the northern coast. Windbreaker and raincoat can be a useful protection from the wind and the rain, especially along the coast and for those who take the ferry for a trip in the fjords. In inland areas, in Oslo and along the southern coast, the temperatures are generally mild, but a sweater for the evening is still recommended. Sometimes it can even be a bit hot during the day, while nights are still cool. In Lapland, the temperatures are a bit more variables, so it can get hot during the day, but also cold at night.
Rain and showers are quite common in Norway even in summer, especially along the western coast. June is a bit cooler than July and August, but it is (relatively) drier and sunnier, and has longer days, with the white nights in the south and the midnight sun in the north.
For skiing, the month of March is better than the winter months, because the temperature is less cold and the days are longer.
The northern islands experience definitely low temperatures even in summer, but at least they are above freezing, albeit slightly.
As mentioned, the ocean, which has a surface temperature of 5/6 °C (41/43 °F) in winter, remains cool during the summer, and reaches 15 °C (59 °F) in August at Bergen, and only 11 °C (52 °F) at Tromsø: it takes courage to swim. It goes a bit better in the Skagerrak strait and near Oslo, where the water temperature reaches 17 °C (63 °F) in July and August.

What to pack

In winter: for Oslo, as well as inland and northern areas: very warm clothes, synthetic thermal long underwear, fleece, down jacket, hat, gloves, scarf. For the west coast: sweater, down jacket, hat, raincoat or umbrella.
In summer: spring/autumn clothes, being ready to add or remove the outer layer, t-shirt, but also long pants, sweatshirt or sweater; jacket, raincoat or umbrella.
For the northern islands: warm clothing, down jacket, hat, gloves, windbreaker, raincoat.