On average across the year, yes, New Zealand is hotter than Svalbard and Jan Mayen . New Zealand has an average temperature of 13°C/55°F and Svalbard and Jan Mayen has an average temperature of -1°C/30°F.
New Zealand's hottest month is January, with an average maximum temperature of 23°C/73°F, which is hotter than Svalbard and Jan Mayen's hottest month (July, with an average maximum temperature of 9°C/48°F).
On average across the year, no, New Zealand is not colder than Svalbard and Jan Mayen . New Zealand has an average minimum temperature of 8°C/46°F and Svalbard and Jan Mayen has an average minimum temperature of -3°C/27°F.
New Zealand's coldest month is July, with an average minimum temperature of 4°C/39°F, which is not colder than Svalbard and Jan Mayen's coldest month (March, with an average minimum temperature of -10°C/14°F).
On average across the year, yes, New Zealand has more rain than Svalbard and Jan Mayen. New Zealand has an average annual rainfall of 953mm and Svalbard and Jan Mayen has an average annual rainfall of 503mm.
New Zealand's wettest month is June, with an average monthly rainfall of 106mm, which is wetter than Svalbard and Jan Mayen's wettest month (September, with an average monthly rainfall of 70mm).