Snow? Maybe, hard to tell. Chances can be good.

Sneakers and clothes? Anything warm and I suggest boots, especially for cold weather.

Hiking? Only if you're an expert with gear. There maybe some basic trials but if there is snow, they may have trials or even the road to the trials closed. The amount of snow that can come down can be significant.

Fishing. Maybe? Depends. Ice fishing is a thing in New Hampshire but lakes need to be have enough ice. Some communities drain the lakes in the region for the winter preparing for the inevitable freeze. Same for ice skating, though there maybe an ice skating rink around the community, you'll have check hours of operation though.

Pizza. Frankly, there is good and bad pizza to be found everywhere in New England. If you're traveling to NYC, the best pizza is believed to be in Connecticut at a place called Pepe's, IIRC. There are actually a few well known places in Connecticut and that state's sub regularly have posts about these establishments.

For Christmas events, you'd have to check around the community.