Mechanically, in fact, there's no reason at all a camcorder can't or won't work in even sub-zero weather. There are just so few moving parts in those things, there's little that can freeze up. The main problem is with the batteries. Electrons move more slowly when cold, so when batteries get cold their effective output greatly drops even if the battery is new or fully charged.
So, here's what you do. First, keep the camera as warm as possible. Carrying it in a camera case that is held close to your body, or maybe tucked inside a ski jacket, should do the trick nicely. You don't want the camera to get too warm, however, or you may have problems with condensation when you take it out to shoot. And, carry a spare battery, keeping it in your pocket or some other warm place. Swapping that battery for the chilled one in the camera, several times a day, should ensure you're never without juice.
Also, many camcorders have a "dew" warning indicator that comes on when there is internal condensation, which could damage the video heads. So check the manual of whatever camera you get to see if it has such a thing, and what the manufacturer recommends when the warning comes on.
As for which camcorder to take along, I'd make a couple of recommendations. One is the Sony DCR-HC65 ($800 U.S. retail, street price of about $600; www.sony.com). It's a MiniDV digital camcorder with a Zeiss 10x optical zoom, big LCD screen, and good battery management features. Very compact—about the size of a paperback book. You might compare it with the Canon Optura 40 (about $800 street price; www.canon.com), another MiniDV camera with a 14x zoom and Canon's Digic DV image processing, which electronically enhances the picture. This is a very nice little number.
Want to make your own DIY ski-porn? Check out Outside's 2005 Snow Report for all the hardware you need for slopeside filmmaking.