Hi BNK9,
Some travel with frig on, some with it off. The main thing to be concerned about is refueling your truck near the open flame on the back of the refrigerator when it's running on propane.
If you are pumping gasoline, you need to shut off the refrigerator before pumping. Gasoline vapors are very explosive. Diesel less so, but many people, and all fire safety people would say to shut off the frig anytime you're refueling, any kind of fuel.