Map from Google - Alaska

Alaska, the largest of the United States with more than 1.7 million km2, largely deserves its reputation as an icy land, but it also has maritime and wet areas, less cold than you might think. Given its size and the fact that it's detached from the rest of the United States, we will treat it separately.

The northern and western coasts and the islands of the Bering Sea (St. Paul, St. George and St. Lawrence) have a subarctic climate, with frosty winters and short summers, which remain very cool if not cold. This is the area of the tundra. Along the northern and the north-west side, up to the Bering Strait, the temperatures are lower than the western coast, especially in winter, both for the higher latitude and because the sea remains frozen for many months. In addition, this area is influenced by the frigid Siberian air masses, which can easily arrive here, moving from west to east.
At Point Hope, on the north-western tip of Alaska, the average temperature in February (which at these latitudes is the coldest month) is -23 °C, while that of July is 7.5 °C. On the north coast, at Point Barrow, it ranges from -25.5 °C in February to 5 °C in July, while further east, in Barter Island, it ranges from -28.5 °C in February to 5 °C in July.
Here are the average temperatures of Barrow.
Average temperatures - Barrow
Min (°C)-29-29-28-21-9-121-2-11-20-25
Max (°C)-22-22-21-13-35872-6-14-19

In this coastal area, precipitation, which occur mostly in the form of snow, except in summer, is scarce, being slightly more than 300 millimetres per year in the west, and even less, that is just above 100 mm, on the north coast. Here is the average precipitation in Barrow.
Average precipitation - Barrow
Prec. (mm)4445482526161164117

On the north coast, the sea is frozen solid for much of the year, when the temperature is equal or below -2 °C.
Sea temperature - Barrow
Sea (°C)-2-2-2-2-2-20220-1-2

Along the west coast, as you move south, both the temperature and precipitation increase. In Nome, the average temperature goes from -15 °C in January to 11 °C in July.
Average temperatures - Nome
Min (°C)-19-18-17-10-15873-5-12-17
Max (°C)-11-9-8-3613151391-5-8

Precipitation in Nome amounts to 430 mm per year, with a minimum in spring and a maximum in summer. Here is the average precipitation.
Average precipitation - Nome
Prec. (mm)252515202025558060403025430

In the western part of the coast, the sea is usually frozen from December to April, while the temperature reaches 10 °C in August.
Sea temperature - Nome
Sea (°C)-1-1-1-104910841-1

More to the south, in Cape Newenham the temperatures go from -8.5 °C in January to 10 °C in July; precipitation amounts to 930 mm per year (with a minimum between February and April and a maximum between July and October), while snow (in total 2 metres per year) usually falls from October to May.
In the Alaska Peninsula, which lies further south and therefore has a less cold winter, the vegetation is still tundra-like, that is made of mosses and lichens, due to the summer which remains cold. In Cold Bay, the average goes from -2.5 °C in February to 11 °C in August. Here are the average temperatures.
Average temperatures - Cold Bay
Cold BayJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)-4-5-4-2258862-1-3
Max (°C)1023710131311742

Here precipitation amounts to 900 mm per annum. Here is the average precipitation.
Average precipitation - Cold Bay
Cold BayJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)706055506055658011011010595910

In the central and western part of the Alaska Peninsula, typically the sea does not freeze in winter, but sometimes it can happen, at least on the north coast and during the coldest winters. Here is the sea temperature in Cold Bay.
Sea temperature - Cold Bay
Cold BayJanFebMarAprMayJunJulAugSepOctNovDec
Sea (°C)43234791110865

The Aleutian Islands are even milder, but they still have a tundra vegetation, because of their cold maritime climate, which is reminiscent of Iceland: cold but not too much in winter (the averages are around -2/0 °C in winter) and very cool in summer, with frequent precipitation throughout the year, but especially in autumn. During winter, heavy snowfalls occur. Even in midsummer, the maximum temperatures are similar to those of Cold Bay, around 12/13 °C.

The vast interior region of Alaska has a markedly continental climate, with frosty winters, and short but mild summer, with a few hot days. Here the dominant vegetation is the taiga (coniferous forest).
The cold records of Alaska (which contend with some areas of Canada those of all North America) have occurred in this area, and in particular in the valley of the Yukon and its tributaries, where the cold air during winter easily stagnates, especially after the cold outbreaks from Siberia or the North Pole. Here the temperature reached as low as -62 °C in Prospect Creek, -59 °C in McGrath and Chandalar Lake, -57 °C in Eagle and Tetlin, -56 °C in Arctic Village and Bettles, -52 °C in Fairbanks.
Apart from the records, the climate of this region is, as mentioned above, strongly continental, so that in winter, lows around -30 °C are normal, while in summer, from June to August, highs are around 20/22 °C, with peaks of more than 30 °C, while nights remain generally cool, and sometimes cold. It may seem incredible, but in the centre of Alaska sometimes the temperature can reach 35 °C!
In this area, the temperature rises above freezing around the end of April, and drops again below this point in October.
Here are the average temperatures of Fairbanks.
Average temperatures - Fairbanks
Min (°C)-27-25-19-63101182-9-21-25
Max (°C)-17-12-4716222319130-12-15

Precipitation in this area is not abundant, so that it ranges from 250 to 350 mm per year, with a relative maximum in summer, due to the higher amount of heat, and therefore energy, which is available in this period.
Here is the average precipitation in Fairbanks.
Average precipitation - Fairbanks
Prec. (mm)15105101535555030201515275

In the mountain regions, we find glaciers and permanent snow. The Alaska Range reaches its peak in Mount McKinley, towering with its 6,194 metres. In the mountain slopes exposed to moist winds coming from the sea, every year large amounts of snow accumulate. Due to both the facts that snowfalls are heavy and summers are cool, the snowline is very low: as a matter of fact, in some areas the glaciers, which by their weight tend to slide slowly downward, flow even into the sea.
Mount McKinley

Let us now talk about the south coast of Alaska. Here you can find different microclimates, depending on slope exposure and distance from the sea, but in general, winter is cold (but less than in the continental area) and summer is mild, with highs around 17/20 °C. Rainfall (and snowfall in winter) is abundant in south and west facing slopes.
Anchorage is located in a sheltered bay, so that precipitation amounts 425 millimetres per year; snow falls from October to April (the total amount of snow that falls in a year is still close to 2 metres).
Here is the average precipitation.
Average precipitation - Anchorage
Prec. (mm)202015102025458575503030425

The January daily mean is -9 °C, like in Moscow, Russia, while in July it's 16 °C.
Average temperatures - Anchorage
Min (°C)-13-12-8-15912106-2-9-12
Max (°C)-5-32814182018145-2-4

At Anchorage, and along the southern coast of Alaska, the sea is cold in winter, but does not freeze.
Sea temperature - Anchorage
Sea (°C)6555710131312987

Further east, and south of the Wrangell Mountains, Valdez is famous for being a very snowy city: even 835 cm of snow per year fall, but in the winter of 1989-1990 a total of 14 metres of snow was recorded! The snow is shoveled and piled in heaps as high as houses, which can last until July. Here the average temperature in January is -6 °C, while in July it's 13 °C; rainfall amounts to 1,700 mm per year, evenly distributed, but with a relative minimum in May and June.

In south-eastern Alaska, west of the Canadian province of British Columbia, the climate and the natural environment are similar to that of the west coast of Norway: in the sea a warm current flows (so that its temperature doesn't drop below 7 °C even in winter), and the climate is cold maritime, with abundant rainfalls (and winter snowfalls as well) on the coasts, but also with islands (see the Alexander Archipelago), fjords and deep coves within which there may be more or less humid microclimates, depending on slope exposure.
Here lies the state capital of Alaska, Juneau, which has freezing winters (the average in January is -2.5 °C), and cool summers (with highs in July of about or 18 °C).
Average temperatures - Juneau
Min (°C)-5-4-215810973-2-4
Max (°C)02491417181713831

In Juneau, precipitation is abundanti, being about 1,600 mm per year, with a peak from August to December, snowfall is abundant and occurs from late October to early April (2.2 metres per year). March and April are the sunniest months, while September, October and November are the cloudiest ones.
Here is the average precipitation.
Average precipitation - Juneau
Prec. (mm)135105957585851151452202201501501585

At Juneau and along the southeast coast, the sea temperature is similar to that of Anchorage and the south coast.
Sea temperature - Juneau
Sea (°C)66678101213121087

If down to a certain latitude precipitation occurs in the form of snow for many months, so that the snow depth can be remarkable, in the southern part it can occur in the form of rain even in winter. In Ketchikan, the southernmost city of Alaska, precipitation amounts to almost 4 metres per year, with a maximum in October (when even 565 mm of rain fall), and a minimum in June and July (when rainfall is still about 190 mm per month). Throughout the year, "only" 1 metre of snow fall (from November to March), certainly not much compared with the huge amount of precipitation that occurs in the cold half of the year.
Here is the average precipitation.
Average precipitation - Ketchikan
Prec. (mm)3503252852852351851902753605654403953890

The average temperature in Ketchikan ranges from 1 °C in January, to 14.5 °C in August.
Average temperatures - Ketchikan
Min (°C)-2013581111851-1
Max (°C)4561013161818151064

When to go

In general, the best season to visit Alaska is summer, from June to August. It's cold along the northern and north-western coast, but at least it's above freezing. It's very cool on the remaining western coasts and the islands (with a daily average around 10 °C). In inland areas, it's mild to warm during the day, and sometimes even hot, but at night it gets cool, and sometimes even cold. In the southern coast, where the major cities (Anchorage, Juneau) are located, the air is mild, but you should be equipped for the cold when embarking (maybe to spot orcas and whales) or approaching closer to the glaciers.
June is the best month in most of the country, except the north coast: it's just cooler than July and August, but more sunny, and has fewer rainy days. However, in the northern coast, where normally it doesn't rain much, in July and August you can take advantage of a temperature a little higher (see the averages of Barrow). Recall that in Alaska the summer declines pretty quickly, so that usually July has more rains than June, and August more than July.
During the thaw (April in the south, May in inland areas, June in the northern coast), the turning of snow into mud makes difficult travelling outside of towns and cities.
To visit Alaska in its winter look, February and March, usually quite sunny in the central and northern regions, are preferable to December and January, because they have longer days.

What to pack

In winter: cold weather clothing, especially for the interior region, synthetic thermal long underwear, fleece or synchilla, down filled parka with insulated hood, wind jacket in Goretex, warm boots, hand and foot warmers, liner socks, fleece socks. For the south-east, less heavy clothes, sweater, down jacket, rain jacket or umbrella.
In summer: clothes for spring and autumn, T-shirts for hot days, jacket and sweater for the evening. For the north, the mountains and for hiking in the sea or in glaciers: rain jacket, down jacket and warm clothes.