ATF (automatic transmission fluid) mixed 1/3 to 2/3 odorless mineral spirits (paint thinner); also works great as a bore cleaner for everything short of removing copper deposits.
This is just a simplified version of the very well regarded 'Ed's Red'.
The ATF has lots of anti-oxidents and when thinned out gets in well and once the carrier has evaporated off it leaves a strong, thin layer of lube/protectorant.
If its that cold out Im not, so I cant tell you how it works in extreme cold. I think if I had to be there it would be with a clean and dry piece (not that many rounds to be fired) or a dry lube.