12 volt Refrigerators are some pretty efficient units , or at least can be. Many people have preconceived ideas based on old tech. 400 watts solar with a sufficient battery pack and no additional large draws would be plenty for a 10 ish cubic foot modern 12 volt unit. Now if your camping in the winter with no sun and furnace use ... well most likely not.
How much battery capacity ?, that tells you how long it will run. the solar or Generator (what solar is)just replenish the battery. hopefully 5-6 hours of solar replenish the 24 hour draw.