Boondocking at a National Forest

For boondocking, as has been said, most RV refrigerators are designed to also run on propane as well as electric. As also said, if you are trying to limit generator time then you need to conserve battery power. The fridge will use a very small amount of battery power but not enough to worry about. If it gets cold and you have to use the heater it uses propane also but it uses lots of battery power to run the blower. You can recharge during the day using the generator but you may have a dead battery by morning if you use the heater all night on just battery power. If at all possible, limit battery use to just the basic systems and a couple of lights when you need them, and you could actually last most of your boondock time without running out of battery.
By the way the battery to start the vehicle is separate from the batteries that run the rest of the RV so you don't have to worry about not being able to start the RV when you are ready to leave.