In the frozen north of over thirty years ago, I used that new product WD-40. After cleaning the rifle, I put a slight amount of WD-40 on moving gun parts and in the barrel.

For those seeing frozen winters, I'd recommend some WD-40 on keys, then into a frozen lock, to unfreeze the lock. I always kept some in the house and in the vehicle, just in case. I found it very useful to change a tire and get the lug nuts unfrozen.