Does anyone have any experience with the carbon AR's in the cold? I live in Alaska.

Yes I do............  I went to a friends house in N.C. in the sticks and was able to fire my bushy 97s....I had some difficulty getting it to feed............. jam after jam........ The problem was that my fire pin was not cleaned properly(my fault) lots of grud.......... I broke it down cleaned it......Put a lite layer of lube on it same w/ the bolt........No futher problems clip after clip, and my beta ran great...... Just make its clean with lite lube on moving parts.....Good luck..........

Use a synthetic gun oil on your Bolt carrier group.  Best advice I can give.  The AR-15's will ALWAYS have issues in sub-zero weather unless you keep the parts lubed with light synthetic oil.  I use EEZOX in the winter.