Couldn't you put frozen food outside, in the snow (at least until the sun comes up)?

Yes, you could, and if you cover it in snow, it should be all right when the sun comes up. My family has used the 'outdoor refrigerator' many a time (though technically that was the garage, but the concept is the same).

Of course, for lavendertook, I don't know that there's a place outside that she could put stuff without risking animals or other people making off with it...