We have camped many times in temps down to what you're describing. We do not have any additional heaters under the floor. In the situation you describe, the propane furnace will provide sufficient heat to keep your inside plumbing going. Do not hook up to outside water and expect it to be running the next morning, even with a heated hose it will most likely freeze at one end or the other so you do need to pay attention to "the outside fittings, ie city water connection, shower nozzle." Pete has "bilge heaters" in his unit. Maybe he'll chime in here. Realize though, you would have to have hookups (electricity) to be able to use them.
Even a large tank of water will eventually freeze at 10 degrees but in my experience, simply keeping the basement areas slightly above freezing does the trick and it's not too hard to do. It WILL use a lot of propane so be aware of that. My guess is that if the temperature never got above 10 degrees, the furnace would run pretty much constantly and you could could use up 60 pounds of propane in less than a week. Realistically, probably daytime temps would get to near freezing or above and lessen that propane load.
Running out of propane in below freezing temps would not be fun or safe, but that's why there are wheels on your trailer. If you are not trapped somewhere, move.