Do you have the fridge yet? Almost all tiny fridges are thermoelectric units, which have terrible efficiency. You'd usually be better off getting a compressor-cooler, something along these lines.

To give you some numbers, small thermoelectrics have a ~45 watt continuous draw. Something like an Explorer 300 would be able to run it for about 6 hours. A compressor cooler will draw about the same when running (maybe a little more), but the duty cycle is going to be about 10-20%, and a compressor moves about 10x the amount of heat a thermoelectric does for the same watts consumed, so you might be able to get away with it, depending on insulation, outside temp, etc.