Well, it's not any more cold than the rest of the north-east. But it probably snows more there than say NYC. And I don't know if they have the infrastructure to rapidly clean up snow from streets like larger cities. When I was there, there was a pretty big snow storm. And because of the really bad road conditions, the last two Dartmouth Coach buses were cancelled (3 and 5pm).
Actually, I'd say that Hanover does a better job of cleaning roads than most NE cities. I lived in Ottawa, Canada for a while and Hanover is much, much better at getting the roads cleared. If it snows overnight, even the side streets are clear by about 6 am. I've never been snowed in. The problem with the coach probably had to do with I-89 not being particularly clear, but the Hanover/Lebanon area deals with the snow very well.
Also, I've lived in Portland, OR and I went to undergrad in the San Francisco Bay area. Yeah, winters in Hanover take some getting used to, but they're really not that bad. It doesn't get particularly cold very often (it'll drop below 0 F a few times per winter, but not too often). That may sound very cold, but it's really not.
Also, some people ask about living out "in the middle of nowhere." Yeah, we're not in a city, but this is a very metropolitan middle of nowhere because Dartmouth has such a huge impact on the area (Dartmouth is the second largest employer in the state and, by far, the biggest employer in the area). You get many big city amenities (arts, famous speakers, performances, athletics, etc.) due to the college without the hassle of living in a big city (traffic, crime). You are also in beautiful surroundings. I would honestly take living in Hanover over the SF bay area any day. Portland vs. Hanover is a toss-up. If you need to live in a huge city, this isn't a school for you. If you enjoy the outdoors, though, I can't think of a better place to go to med school.