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There are numerous threads on this if you do a search. The advice is pretty constant:
1. Condensation when going from cold to warm - leave the camera in a bag until its warmed up. Don't be tempted to take out memory cards, change lenses etc until it is warm (do this before you go inside).
2. Battery power - keep them warm.
3. Keep your hands warm - cameras are metal, and in very low temps frostbite is a real possibility.
4. At close to 0C snow is wet and soft. Below maybe -5C it is hard and abrasive. Bear this in mind when getting snow on your camera and lenses, and when you clean it off.
Also, more specific to the snowmobile aspect:
5. Hard and/or pointy objects in pockets and bags can cause ruptured kidneys, splein etc in the event of an accident. This is probably as true for snowmobile accidents as for motorcycle accidents.
6. Keep yourself warm. I've seen a test comparing motorbike control when extremely cold and when very drunk. You have less control when cold.