I would carry along a MR BUDDY 1lb propane canister heater (LOWES-WALMART) and use the POPUP furnace as a back-up. The furnace fans draws around 6-8 AMPS DC and thats alot of drain if you plan on running it all night long. We also heat a big pan of water on the stove...
The MR BUDDY heater will run around 7 hours on one propane canister. We sit our Mr Heater on a shelf we use and just open the roof vent right above it a tad. Keeps us warm and snug all night and safe to use. We also have one of the AC/DC O2COOL 10-inch fans (LOWES-WALMART) to move the air around the POPUP.
We also use an electric blanket which is run by an inverter but you have to plan for these kinds of things with your whole battery system to be successful about it and not run out of battery in the middle of the night. My battery system includes a smart-mode Converter/Charger, LED replacement boards, Inverter, larger battery cables, additional batteries, to operte all we want to use when camping off the power grid in a one day/night experience. Then we re-charge our battery bank with a 2KW Honda generator to 90% charge state in 2-3 hours the next morning during breakfast so we can do this all over again for the next day/night camping experience.
sample photos from google images