Having spent 2 winters in my RV, weathering -20ºf in Idaho and Montana, I have a bit of input. My 5th wheel is 24', true 4-season Northwood.
The first winter I went unskirted. No added interior insulation on windows, etc. Floor was crazy cold, I had a lot of rugs and mats. I relied mostly on electric heat. Using propane heat, a 7 gallon tank would last 3 days in the worst cold and the furnace ran near constantly. I fell back on electricity mostly because it was less wear and tear on the RV's systems and also it was nearly silent. I could barely sleep when the propane heat kicked on. To keep nighttime heating at a minimum, I closed the overhang bedroom off (there's a panel "door" to the bedroom) from the rest of the 'house'. This kept the heat in the main body of the RV instead of it all floating up into the bedroom. I slept with sleeping bags, blankets, and warm 4-legged space heaters. Mornings in the bedroom were cold, but the rest of the 'house' was warm, and this method kept my power bill down. A simple 750/1500 space heater worked just fine. The one I had was even a mock fireplace with fake flame aesthetic, the ambiance was a huge morale boost.
To handle the water, I kept the water heater running, of course. On the coldest nights I let the faucets dribble. If it got below 10ºf I had to heat the pump or it would freeze up. So I bought a water-proof rubber heated "work mat", it was made for relief from standing on cold floors, so it was rugged. I laid this over my water tank and turned it on when it got below 20º. I couldn't put it too close to the pump or it would overheat the pump. But draped over the water tank, it worked perfectly.
Edit: To keep drain lines from freezing in the worst temps, following up with piping hot or near-boiling water is a really good idea. Once, in my first winter, I accidentally left a grey water line closed and it froze. My kitchen water line was backed up and frozen. All water dumping had to switch to the bathroom grey water line until it warmed up enough to melt the kitchen grey line.
Yes, a few nights my pipes froze regardless, both winters. I had to be prepared to deal with hauling and conserving water.
My grey water flowed freely into a gravel-filled hole. I don't use anything chemical or toxic, it's all garden-friendly waste water. My first winter, my black water had to be manually emptied into 5 gallon buckets and carried about 150' to the septic tank access. I'd open the cap to the septic tank and dump the buckets in. That was always bath day. It was gross, but I had no choice. Got really good at not sloshing the buckets. It never froze on me that I can remember. I only had to empty it once every 4-6 weeks though. It might have frozen during the coldest stretches and I just didn't notice because I didn't have to mess with it at the time.
My second winter, I let pee drain with the grey water. One person's worth, mixed with water, into a drainage trench wasn't a big deal. Still perfectly garden-friendly. I pooped in a nearby building with a proper toilet. Made the septic situation hassle-free.
My second winter, I was smarter, and it was colder. I skirted with straw bales. It took nearly 2 tons to do, $300. The floor was so much warmer! I composted the hay the next year. I insulated all of my windows with 1 or 2 layers of bubble wrap. This allowed light to come in but kept the cold drafts out completely. Mild mold crops, nothing too serious. The window frames needed a good deep cleaning in the spring. I also insulated around the door, and even bubble-wrapped the screen door so I could leave the front door open without all the warmth gushing out. I bubble-wrapped my sky lights. Etc etc. The RV was much more comfortable, and it was a much colder, longer winter with way more snow (Montana winter). I kept my roof shoveled every 12" of snow or so.
Of course before my first winter even hit, I re-caulked EVERYTHING. I did not want to deal with leak issues in a rough season, or ever.
The biggest issue both winters was moisture. Condensation. Humidity. The first winter I was doing laundry in my RV and attempting to also dry it in there with the electric heaters. It was a swamp on those days! I ran the vent fans a lot and line-dried whenever I could.
I'm about to do a 3rd winter in the same RV. In a much milder climate this time though, it won't be as tough. This year I'm intending to install a wood stove. I agree that with proper, mindful installation and shielding, there's not a lot of risk involved. Shield above, below, and all around it, and mind your chimney pipe. Know what to do in case of a chimney fire.
I personally want a wood stove to keep it dry, cut heating costs and be more independent, and have the ambience of the fire, the familiar roar of the flames. It does a lot for the morale in a long, cold winter. Chopping wood is good exercise, and it's also a good way to produce free hot water and cook without using propane.
This year I will be skirting with greenhouse plastic. 6-mil heavy stuff, it's pretty cheap at $0.12-$0.14/sq ft on ebay. Skirting will cost less than $100 this year, and the skirting will be reusable and won't take up much room once folded up and stored for the summer. Hopefully it's a good experiment!