Using TV inverter to power fridge while towing Do or don't?

On my Hideout, which I traded in for the Open Range, it stated that the refrigerator wasn't to be set to propane when on the road. And, sure enough, the few times I tried, it stopped working sometime during the tow. It said to run on DC when being towed, which would have caused one very dead battery. I'm guessing that the OPs refrigerator is similar to my old one. Thus, the ice chest to keep stuff cold while towing.