Using the calculator linked by Powerdude, even #6 cable will give you 0.7 V drop when you run it via bumper plug, what gives about 30 feet of wires before they reach the camper fridge.
I have another idea. My Ford has build-in 400W inverter and it is a good one as I tested it to run my small air compressor out of it.
So instead of tearing the truck and camper apart to run #2 cables - how about running #14 extension cord from truck 120V plug to refrigerator?
That would also run more powerful 120V fridge element.
I drive with rear window open and inner tube sealing the gap between truck and camper windows, so all I need is to find how to pull fridge plug up front and 8 feet of cheap extension cord will do.
The only trouble I see now is truck alarm going off when I park the truck with rear window open.