What type of refrigeration is recommend in a cabin with sub-freezing temperatures?
You may be able to use a propane or natural gas powered fridge.  They have no moving parts that would break; in the extreme cold, I'd imagine that only the pilot light would be on.

I've stayed in a cabin that had one of these that was regularly exposed to -25 F, and it lasted for 40+ years.

http://home.howstuffworks.com/refrigerator5.htm