Well I don't see anything about how mild or severe of cold if any. You could probably just put an old freezer up against an outside wall, drill a couple small holes and run the cable through the wall into the house. Batteries outside, gases outside, inverter in the house. Cable length pretty close to same as if the batteries were in the cabin.
Unless your thinking of putting the batteries in the center of the cabin, the batteries up against an outside wall should not really be that much more wire than on the same wall on the inside. Do everything safe of course, but I think that's how I would do them. Either through the wall or the floor, which ever works best, but probably only a couple feet of extra wire at most?
Old junk freezer should be free or cheap, insulated already, etc.. Could paint it to blend in and look decent if wanted also.
Might work very well, unless your cabin is high up off the ground.