The very WORST, re cold places in N.H., is on Mount Washington!
OTOH...during college Senior Week ( Seniors took finals before everyone else and we had a full week off, before graduation, to have fun, rest, and attend some special events ), we had a WONDERFUL day and evening dinner dance at the hotel on Mount Washington at the end of May.
During WW II father-in-law was posted to the top of Mt Washington to test cold weather equipment in winter. Brrr.