" One strange thing I did notice is that the fan that I can usually hear cycling on and off every few minutes when things were working normally.....was constantly on in the morning when the fridge wasn't cooling."
If that was the converter acting up and you were actually getting your 12v from the battery, it could be that the battery was too low in the cold by then to run the fridge and it came back up a little when it got warmer so the fridge worked again.
You must have had some 12v to be able to use the fridge controls though.
31F should not bother the fridge itself in either AC or Gas--both need 12v though.
The converter fan should not be cycling every few minutes when "normal" or be constantly on either. It could be the battery making the converter do that. Need to check out your 12v system.
