Cold Soaking
During operation, digital cameras actually generate their own heat. With some early digital cameras, after continuous operation for a while the batteries became almost to hot to touch! Modern cameras are significantly more efficient and generate less heat, but if you can keep that heat in the camera (by not cold soaking it), you may have fewer cold weather related problems.
Cold soaking is leaving a camera out in the cold until every part is at ambient temperature - and it's likely to increase the probability of cold related problems. Since it can take quite a while for a camera to fully cool, if you only expose your camera to the very coldest temperatures when you're shooting, and put it in a pocket or a camera bag when it's not in use, you'll likely have fewer problems then if you leave it permanently hanging around your neck, fully exposed to the cold. It may not be that much warmer in your pocket or your camera bag but every little helps. See also the section "Hand Warmers," below.
One thing to avoid though is bringing a really cold camera under your coat, especially if you've been sweating and the air trapped under your coat is very humid. This can happen even in very cold weather if you have a highly insulating coat and you've been working hard, for example by walking though deep snow. A cold camera/lens in a humid environment can results in condensation of moisture on both the optics and electronics, which is something best avoided. (See also "coming in from the cold" below).