The biggest challenge I face shooting in cold weather (I live in Alaska) is my breath causing condensation/frost on my lens. When I shoot in the winter, I am usually outside long enough that my camera has cooled to ambient temperature or close to it. I don't pack all the chemical hand warmers it would take to keep a camera warm for as long as I go out in the winter. If I am shooting handheld, I usually fight condensation by holding my breath while the camera is to my eye, or at least exhaling through my nose. Never, ever exhale through your mouth with a camera to your face in cold temperatures. Same holds true for shooting on a tripod, I do all my breathing away from the camera, and hold my breath if I need to take a close look.
As has been mentioned, if you are going to be going in and out of a warm space (car, cabin, hotel), keep your camera buried in your bag until it has had time to warm up, or just leave it in there if you are going back out in the cold. You don't need to put it in a waterproof bag. Just leaving it closed up in a normal padded camera bag will give it enough insulation that it can warm to the room temperature without creating condensation. If you are in a car moving from spot to spot, put your camera bag in the trunk.