Refrigerators that are both propane and electric (12 volt from battery or 110 volt from shore power) use a heat
to drive the coolant. Heating elements of any kind draw a lot of power and are best avoided when talking about battery power.
Some people who have tow vehicle set up to charge the RV battery and provide 12 volt power from the tow vehicle charging system to the camper. They might switch fridge to 12 volt operation while traveling. This does require a set up that delivers sufficient charging power to camper to prevent running the camper battery down while running the fridge going down the road.
Others leave fridge on propane while traveling, and some just shut it off while driving figuring like an ice chest it will stay cool for the duration of that days travel. Couple of blue ice packs in freezer that are frozen overnight using propane or 110 volt from campground can help with that approach.
These type of refrigerators are slow to remove heat from inside the refrigerator
, typically taking hours to get fully cold so as Carol pointed out so pre-cooling both the fridge and it's contents before heading out is a good tip.