Correct me if I am wrong, but wouldn't a refridgerator take much more power than a single solar panel could supply? I know there are some efficient refridgerators out there, but a single LARGE solar panel is still only about 125 watts of output under ideal conditions. I am also not convinced a single AGM battery (about 125Ah or so) would be able to keep it going through the dark hours, especially in the winter months when there is limited hours of sunlight.
What do you have against using the conventional RV style gas absorption style refridgerators using propane? My refridgerator can run on 12V, 120V, or propane, and it seems to work very well.