On average across the year, yes, New Hampshire is hotter than Wisconsin . New Hampshire has an average temperature of 9°C/48°F and Wisconsin has an average temperature of 8°C/46°F.
New Hampshire's hottest month is July, with an average maximum temperature of 29°C/84°F, which is hotter than Wisconsin's hottest month (also July, with an average maximum temperature of 28°C/82°F).
On average across the year, no, New Hampshire is not colder than Wisconsin . New Hampshire has an average minimum temperature of 3°C/37°F and Wisconsin has an average minimum temperature of 3°C/37°F.
New Hampshire's coldest month is January, with an average minimum temperature of -9°C/16°F, which is not colder than Wisconsin's coldest month (also January, with an average minimum temperature of -12°C/10°F).
On average across the year, yes, New Hampshire has more rain than Wisconsin. New Hampshire has an average annual rainfall of 1196mm and Wisconsin has an average annual rainfall of 978mm.
New Hampshire's wettest month is October, with an average monthly rainfall of 130mm, which is the same as Wisconsin's wettest month (June, with an average monthly rainfall of 130mm).