Electric heat is indeed the best in a small trailer: quiet and steady versus the noisy cycling of a furnace
. It also has the advantage that it comes in an unlimited supply, as most campgrounds do not meter the power.
However, it's not really free. In a poorly insulated trailer, you are using a shared resource very inefficiently. For a night or two here and there, fine. As a long-term, cold weather solution, not so good. The same could be said of heavy A/C use in hot weather.
you become a lot more aware of your energy footprint. If you are burning through a tank of propane
every other day, you will soon be looking for a trailer with better insulation. There aren't many. Some resort to building their own or doing a complete renovation
to super insulate.
Or focus on travel to mild weather locations according to the season.