Let's say SHTF and you are surviving, not camping...
Save batteries at all cost! If, IF you have enough solar to run an electric heater and have extra to also charge batteries to full during the day then that is an option only during the day and will save propane (because SHTF and propane no longer available).
The furnace fan will use a lot of battery overnight also, so that will deplete batteries. Yes, u can just recharge batts the next day on solar, but every time u deplete a battery it dies a little.
True camping means getting a sleeping bag that will keep you warm. You can stay toasty warm at 10 degrees in a bag with no external heat. In the day time you will be moving around so would want heat then if you are stuck in the camper.
I would never, even in prosperous times, use batteries to heat a camper.
