Keeping the camera warmer than the outside temperature isn't as hard as it sounds. When it's very cold, it's also often clear and sunny (night's another story, of course). So keeping the unit in a camera case inside a backpack, which the sun will warm a little, can make a big difference. It's also extremely helpful to zip the camera inside your Gore-Tex parka or down suit. Most lenses for 35mm SLR cameras have a manual override, so if for some reason the autofocus gets sticky, you can still focus the old-fashioned way.
Pay particular attention to the batteries; carry lots of them, and rotate them regularly, keeping the spares in a pocket. Batteries don't die quicker in the cold, but if they do get cold, the electrons inside literally slow to the point where they can't "escape" from the battery.
Generally, I think the better cold-weather cameras have fewer electronic parts. Cameras that are mostly manual, such as an older Canon F1 or Nikon F2, would work well, and can be "winterized" by a good photo technician (a process that involves removing some lubricants and swapping out others so they can't freeze and gum things up). They also have the advantage of allowing manual rewind, useful because cold film can be extremely brittle and prone to static if rewound or advanced too quickly. Point-and-shoots, while compact, aren't so good because most rely so heavily on automatic rewind and the like.