I lived in a travel trailer for a year in an RV Park in Anchorage, Ak, sadly, it was an unusually cold year and it was a truly miserable year! The previous 6 years I had lived in a box van in Anchorage and was 1000 times more comfortable even though some of those winters were even colder!! How can that be? It's so easy to insulate the straight walls and roof of a box van it was able to heavily insulate it and hold the heat I made inside. It had no windows and I was able to make the doors pretty air tight so it had little air infiltration.
Nearly ALL travel trailers will have pathetically little insulation and many windows and openings that will leak like a sieve! Denver isn't as cold, but it will still be very unpleasant. Jim in Denver gave you great advice, let me add my thoughts:
1) Like he said, don't try to keep the water running, shut t off, winterize, and use the Parks facilities. That's just what I had to do.
2) Almost certainly a Propane store will deliver a bigger bottle, like 100 pounds or more, and then refill it over the winter, call around. You can buy a 100-pound bottle for not much, less than $100 i think. Then sell it when you're done.
3) Add insulation and weather sealing everywhere you can. Also, you'll want skirting, preferably styrofoam.
4) I recommend 500 watt heat lamps that are moveable so you warm the area where you are and not try to heat the whole space. My furnace simply could not keep up with the cold and the heat lamps made my time bearable. Aim them at your feet because the floor is impossible to keep warm and then the heat will rise and warm the rest of you.
5) My poor, old furnace ran about 20 hours a day when it was -30 and I was afraid it would just wear out, so I'd also recommend Olympian Catalytic heaters to supplement the RV furnace so it got a break.
Finally, give thought to getting a cargo trailer instead. You can add enough insulation to it to stay very comfortable all year. 4 inches of polyiso all the way around and you can easily be toasty with an Olympian Wave 8. Since you will be using the Parks bath house instead, you won't miss the plumbing. You can easily add everything else with used furniture, and camping gear. No building required unless you want to. The RV Park won't like that, but maybe if you commit to getting a real trailer come spring, they would allow it for the winter. They are usually more tolerant over the winter when the park is usually fairly empty.
Hope this helps