Well, I think everything that can be said on this subject has been except one:
The quickest way to ruin a $2,000 fridge is to run it on a small generator that barely makes enough amperage to handle the load. I learned this the hard way years ago, on my first hurricane after we moved to Houston. I had previously picked up a small generator at Northern Tool that I calculated should have been capable of keeping my fridge and freezer running, plus a fan, a TV, and a lamp. Every time the fridge or freezer would kick on, the generator would bog down, obviously working hard to keep up with the load. In order to stretch our gasoline supply, we'd shut everything off every four hours, and over night. About a week in, the fridge just quit coming on. At that point, we threw in the towel, gave all the meat to the neighbors, and moved in with our San Antonio kids for the duration. The repair bill was about $500 -- more than I paid for the generator.
After that experience, about the only thing I'd try to run off that cranky ONAN in the RV would be the stuff in the RV. If all I had to keep my house from freezing was that generator, I think I'd drain the water lines in the house and move into the RV.