If indeed you do not have heat going into your bays things could get pretty cold. Your only hope is to add a lightbulb or small heater but care must be taken to avoid starting a fire from either of those being too close to something flamable.
And, as previously mentioned...if you will be boondocking you will need to run the generator 24/7 for your furnace and any heating device down below. Most generators use approx. 1/2 gallon per hour so plan to have plenty of fuel on hand. Your battery bank won't support the load of the furnace and heater running for more than a very short time.
Do a search on winter camping on this website and you'll find more info than you can read in a week!
The best thing winter travelers can do is buy a mini weather station with remote sensors. We keep one sensor in the water/utility bay to monitor the temperature in there. If that reading drops below 32 for more than a couple of hours we put a 60W drop light in there to keep the pump from freezing. That plan has worked for us down to sub-zero. The other sensor is behind the drawer of the generator up front so we have an idea about outdoor temp.
Another area to watch is your ice maker if you have a 2 way absorption/RV type refrigerator. The valve is on the back of unit exposed to outdoor temps and will easily freeze. After replacing 2 of them and realizing we don't like "tank water ice cubes" we took ours out. However you can shut off that water line and drain it so it will not freeze.
One thing you should not do is keep any faucet dripping to prevent freeze ups. I know folks do that in a stick house but all you'll do in an RV is run the pump more and fill up your waste tank. If hooked up to a dump site with the dump valve open it will fill up the dump hose with ice and make it impossible to drain.
Enjoy you winter holiday! If it were me, I'd give it a try but if running the generator is too expensive or a hassle you might have a back up plan--find a nearby RV park.