A dozen years ago, when I started RV'ing, I pondered this same question. Turn refrigerator off while traveling, or leave on. I admit that a vented gas flame,contained in a little galvanized sheet metal enclosure, hurling down the highway at 60 MPH was of a concern to me. I even rehearsed in my mind how to do an emergency unhook on the roadside when the I looked in the rear view mirror and saw the trailer blazing.
Alas, that was about 60,000 miles ago and I have never had a problem letting it run.One of the deciding factors was a grouchy wife when the ice cream got soft.
