I would submit that a gun in good working condition needs NO oil in cold weather. If it is clean and smooth working, then it should operate better BONE DRY than with any lube on it. A little graphite is better in sub-freezing temps...in my opinion.
If any gun is working roughly when completely void of oil, but seems to work a little better with some lube...then that gun needs some buffing and polishing...maybe more.