Battery power in fall

With a single battery you'll be able to run it one night AND if it's not so cold that it would cycle 100%.
Run furnace a few hours before bed time only. Then you'll have some juice left for tomorrow.

Furnaces are terrible in terms of energy use.

Probably pushing it for a single battery set-up, a pair of fully charged batteries will fare much better under this scenario. Of course it all depends on how long furnace is run daily and how many amphours other DC powered items are consuming. A general rule of thumb is roughly a battery a day when extended furnace use is expected, adding some solar can keep you going for days.

Also will depend on what you want your thermostat set on/how warm do you want to keep the inside?

When I camped at the race tracks, I would be lucky to get a night on a battery and heater when it dipped into the 30s.

We are pretty good on here and yes I see you have a fairly new camper BUT how many AH is your battery or is it your batteries?

Depends on the battery capacity BUT since you are asking the question, in all likelihood, the answer is NO.

how many batteries? what is it's/their capacity?
bumpy