Welcome to iRV2, mnreject. Is this just the wiring that feeds the fridge? If so, it is pretty simple - a 12v wire and a 120v outlet that the fridge plugs into. But if it burned, i suspect the problem is wider spread than that, perhaps destroying the numerous wires on the fridge controller itself. That is fridge wiring rather than Southwind wiring, and you need to identify the make and model of the fridge.
Could you possibly attach a picture of the damaged area? Hard to give any helpful hints without being able to see what wiring you are talking about.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL
Summers in Black Mountain, NC