Ditto to elks and rainshadow. Can't emphasize enough that condensation is the big problem if you have cleaned and removed oil as I think mleon said. Get the trigger assembly, inside of bolt and firing pin oil free for extreme cold.
Condensation is harder to combat. Jumping in and out of a vehicle in cold weather with a heater going is the toughest test for waterproof scopes and for keeping the inside of the bolt free of ice. As rainshadow says from experience, in our world we keep rifles outside of tents, cabins, vehicles as much as we can and leave them outside overnight. They are OK if they stay cold and away from warm moist air. Unless theft etc. is a problem only bring a rifle inside during a hunt if it is going to stay long enough to warm up and then dry out completely before going outside again. Condensation forms on the cold metal when it comes into warm air.
I've had a firing pin fail to hit hard enough to ignite a primer two times due to cold. One was from oil I think, and the other was definitely ice inside the bolt. Both times I ejected the round, which had a tiny dimple in the primer, chambered another round and in both cases the second round fired.
The one with ice was aimed at a very nice 6x6 bull elk. It had rained a little the day before and frozen hard during the night. Though dried the evening before, enough moisture was inside the bolt that when I squeezed on the bull just after daylight, I heard a soft "chinnk" of ice being crushed by the spring and firing pin. I knew instantly what had happened and tried a second shot hoping the first one had broken enough ice to let the firing pin fall. It had.
The other foiled shot was on a coyote in dry cold. I think that was oil because it would fire about 2/3 of the time. A friend's rifle.
I never tried the Rainshadow dance with bolt inside my coat under armpit but that would work. Thanks for the new trick. If you have time, that is more sure to work than merely shooting again as I did.