Map from Google - New_Zealand

In New Zealand, divided between two main islands, the climate is oceanic, mild in the north and cool in the south, and also windy and rainy especially in the southern and western regions. The weather is often variable, so that there can be the sunshine and rain alternating in a few hours. Both the summer heat and the winter frost are rare, except in the far south, where the winter can be cold.
The rains are quite frequent throughout the year, but they are usually more frequent in winter than in summer, except in the extreme south (see Invercargill), where they are frequent even in summer.
The amount of sunshine is never exceptional, but it's still acceptable in summer, at least in the north, where there is a good number of sunny days.
Being in the Southern Hemisphere, in New Zealand the seasons are reversed compared with Europe or North America.

The North Island has a mild oceanic climate.
In Auckland, the average temperature goes from 20 °C (68 °F) in January and February to 11 °C (52 °F) in July and August. Here are the average temperatures.
Average temperatures - Auckland
AucklandJanFebMarAprMayJunJulAugSepOctNovDec
AucklandJFMAMJJASOND
Min (°C)161715131188810111315
Max (°C)242423201715141516182022
Min (°F)616359555246464650525559
Max (°F)757573686359575961646872

Rainfall is fairly abundant, since it amounts to 1,250 millimetres (49.5 inches) per year, and is well distributed throughout the year; however, the rainiest season is winter, when rainfall exceeds 100 mm (4 in) per month, from May to August. Here is the average precipitation.
Average precipitation - Auckland
AucklandJanFebMarAprMayJunJulAugSepOctNovDecYear
AucklandJFMAMJJASONDY
Prec. (mm)8095809512513514511510010090801240
Prec.(in)3.13.73.13.74.95.35.74.53.93.93.53.148.8
Days77810141416141311108132

At Auckland the temperature of the sea is very cool, however, it reaches 21 °C (70 °F) in February and March, when those who do not suffer from the cold, can try to swim.
Sea temperature - Auckland
AucklandJanFebMarAprMayJunJulAugSepOctNovDec
AucklandJFMAMJJASOND
Sea (°C)202121191817161515161719
Sea (°F)687070666463615959616366

The capital Wellington is located on the Cook Strait, which separates the two islands, and it's very windy. Winter is mild, given that the average temperature in July is 9.5 °C (49 °F). Summer is cool: the average of January and February is 18 °C (64 °F). Here are the average temperatures.
Average temperatures - Wellington
WellingtonJanFebMarAprMayJunJulAugSepOctNovDec
WellingtonJFMAMJJASOND
Min (°C)15151412108779101114
Max (°C)212120171513121315161820
Min (°F)595957545046454548505257
Max (°F)707068635955545559616468

The annual precipitation amounts to 1,200 mm (47 in), therefore it's similar to that of Auckland. The rainiest period is from May to August, which is also the one with the most frequent rains (11 to 13 days per month) and the least amount of sunshine (3/4 hours of sunshine per day). Even in summer, however, it rains an average 7/8 days per month, except in February, when the days with rain are only 6. Here is the average precipitation.
Average precipitation - Wellington
WellingtonJanFebMarAprMayJunJulAugSepOctNovDecYear
WellingtonJFMAMJJASONDY
Prec. (mm)808080951151151351159510090901190
Prec.(in)3.13.13.13.74.54.55.34.53.73.93.53.546.9
Days76891112131210998114

The sea temperature in Wellington is always cold, however, it reaches 17/18 °C (63/64 °F) from January to March, as can be seen in the following table.
Sea temperature - Wellington
WellingtonJanFebMarAprMayJunJulAugSepOctNovDec
WellingtonJFMAMJJASOND
Sea (°C)171817161514131313131416
Sea (°F)636463615957555555555761

In inland areas of the North Island, there are hills and even a mountain, Ruapehu, where you can ski in winter, and on top of which, above 2,500 metres (8,200 ft), there are eternal snows.

Wellington

The South Island is cooler, and is exposed to the westerly winds that blow for most of the year. In winter, however, snow and frost may occur, especially in the southern part, due to cold air masses of polar origin. This island is crossed by the Southern Alps, culminating in Mount Cook, 3,754 metres high: the western side is definitely wet, in fact precipitation goes from 2,000 to 3,500 mm (80 to 140 in) per year along the coast, and it's even higher on the western slopes, where it touches even 6 metres of rain per year, while the eastern side, where the main cities of the island are located, is definitely less rainy, so that precipitation decrease below 1,000 mm (40 in) per year, and some inland areas are even arid: in Alexandra, only 330 mm (13 in) of rain per year fall.

In the mountain range, there are eternal snows above 2,000 metres (6,500 feet). In the central and southern areas of the South Island, there are glaciers that descend from the mountains almost to sea level, and after having turned into rivers, flow into the sea or into lakes.
Christchurch, located on the east coast, receives 640 mm (25 in) of rain per year, and is the least rainy between the major cities of New Zealand, even though the rains are quite frequent. Here is the average precipitation.
Average precipitation - Christchurch
ChristchurchJanFebMarAprMayJunJulAugSepOctNovDecYear
ChristchurchJFMAMJJASONDY
Prec. (mm)554550506565705045455055645
Prec.(in)2.21.8222.62.62.821.81.822.225.4
Days75678998777787

The average temperature goes from 17 °C (63 °F) in January, to 6 °C (43 °F) in June and July. In this as in other cities of the eastern side, sometimes there can be sudden rises in temperature, due to downslope winds that descend from the mountains.
Average temperatures - Christchurch
ChristchurchJanFebMarAprMayJunJulAugSepOctNovDec
ChristchurchJFMAMJJASOND
Min (°C)1212107411246811
Max (°C)232220171412111215171921
Min (°F)545450453934343639434652
Max (°F)737268635754525459636670

On the western side of the South Island, winds are frequent and intense, especially in the south-west, the area of the fjords. As mentioned, we are in fact in the area of the westerly winds that sweep the southern seas around Antarctica.
In the far south, the climate is very cool, if not cold in Invercargill, where the average temperature is between 14 °C (57 °F) in January and 5.5 °C (42 °F) in July.
Average temperatures - Invercargill
InvercargillJanFebMarAprMayJunJulAugSepOctNovDec
InvercargillJFMAMJJASOND
Min (°C)1098642124679
Max (°C)191917151210101113141618
Min (°F)504846433936343639434548
Max (°F)666663595450505255576164

The rains in Invercargill are frequent throughout the year, as well as wind and cloud cover. Here is the average precipitation.
Average precipitation - Invercargill
InvercargillJanFebMarAprMayJunJulAugSepOctNovDecYear
InvercargillJFMAMJJASONDY
Prec. (mm)10585100105110908080801051051001145
Prec.(in)4.13.33.94.14.33.53.13.13.14.14.13.945.1
Days12911121312121110121311138

The city of Dunedin, which is located in the south-east, is a little more sheltered from rain and wind, but all in all it has a similar climate.

The coldest cities in winter are those located in the southern inland areas, such as the aforementioned Alexandra, which in addition to being dry, is also cold, with only 3 °C (37.5 °F) of average in July. Here, during cold waves, there may be intense frosts at night.
Average temperatures - Alexandra
AlexandraJanFebMarAprMayJunJulAugSepOctNovDec
AlexandraJFMAMJJASOND
Min (°C)1110842-1-203579
Max (°C)2424211713981215182022
Min (°F)525046393630283237414548
Max (°F)757570635548465459646872

Here the rains are frequent throughout the year but they are scarce, since they don't reach 300 mm (12 in) per year. Here is the average precipitation.
Average precipitation - Alexandra
AlexandraJanFebMarAprMayJunJulAugSepOctNovDecYear
AlexandraJFMAMJJASONDY
Prec. (mm)403030302020101020302030290
Prec.(in)1.61.21.21.20.80.80.40.40.81.20.81.211.4
Days1098111312101210131013131

The temperature of the sea in the South Island is always cold; at Christchurch it goes from 10 °C (50 °F) in the winter months, to 15 °C (59 °F) in January to February. In the far south, in Invercargill, it reaches 13 °C (55.5 °F) in January and February, although during winter it's still about 10 °C (50 °F).
Sea temperature - Invercargill
InvercargillJanFebMarAprMayJunJulAugSepOctNovDec
InvercargillJFMAMJJASOND
Sea (°C)131313121110101010101112
Sea (°F)555555545250505050505254

Let us now have a look at the climate of some islands belonging to New Zealand, but far away from the main territory.
Raoul Island, more than 950 kilometres (600 miles) north-east of the North Island, is mild and rainy. The average goes from 16 °C (61 °F) in July and August, to 22 °C (72 °F) in February. On average, 1,500 mm (60 in) of rain per year fall, well distributed, with a relative maximum in winter and a relative minimum in spring.
Campbell Island, 600 kilometres (370 miles) south of the southern coast, is an uninhabited island, definitely cold and windy all year round, so that the average temperature goes from 9 °C (48 °F) in summer to 4/5 °C (39/41 °F) in winter. Rains are frequent throughout the year, and even snowfalls in winter. The sky is almost always overcast.
The Chatham Islands, 900 kilometres (550 miles) east of the South Island, have a mild oceanic climate, similar to certain areas of the South Island itself, with frequent rainfall throughout the year, though not abundant, and an average temperature of 14 °C (57 °F) in January and February, and 7 °C (44.5 °F) in July.

New Zealand is not located in the path of cyclones, but once in a while a tropical cyclone, usually weakened, may go up to these latitudes and affect the North Island and the northernmost part of the South Island, bringing rain and wind, from November to May.

When to go

The best time to visit New Zealand is the austral summer, from December to March, which is pleasantly warm in the North Island, and cool in the South Island. Wanting to visit the country in the winter, for example in August, you can choose the North Island, being milder and more sheltered from cold waves, maybe combining the exploration of the cities with some skiing in the mountains.

What to pack

In winter (June to August): for the North Island, Auckland and Wellington, spring/autumn clothes, sweater, jacket, raincoat or umbrella. For the South Island, warm clothes, down jacket, scarf, hat, raincoat. For the high mountains, mountain clothing.
In summer (December to February): for the North Island, Auckland and Wellington, and the South Island up to Christchurch, light clothes for the day, a sweatshirt and a light jacket for the evening, raincoat or umbrella. For the south, spring/autumn clothes, sweater, raincoat and umbrella. For the Southern Alps, warm mountain clothing.