Assuming you keep the interior at even a modest 50F and let a little heat leak into the battery box, the batteries won't see anything close to those temps.
Of course, at those temps, lots of issues:
- At around -43C, propane will no longer vaporize. Even at slightly warmer temps, it will vaporize more slowly which can create issue with appliances operating correctly.
- Even if the furnace is operating correctly, most RV's won't be able to keep the interior above freezing.
- Tank heaters and such are likely to be overwhelmed.
- We were in -5F one time and we were going thru a 30lb tank per day...-40F is much colder, so keeping a supply of propane becomes problematic.
RV's have wheels for a reason. They really aren't suitable for those conditions.