Mickey, It truly depends upon ?how cold is cold?! We lived in our old Teton for two (2) Wyoming winters, and saw quite a few -20 to -30 F mornings. We never froze a water line inside the unit. It was only a 34 foot unit with a single (34000 btu Heater I think) and stayed very comfortable. We did have some frost on windows (the old louver crank type) and in a couple places at slide seals. But....it was designed for cold weather use.
For the camper. If you have a heated ( forced air to basement, tank and line area) underbelly. You may not need to heat trace the piping, or put heat pads (generally 12 volt) on your tanks. If your dump valves are ?not? in the heated area, you will need to heat trace and insulate (preferably all the way to the connect). If you do not have dual pane windows, you may want to cover some windows (decide which ones you can live without) with ?quilted? foil type insulation. Your heat loss through single pane is pretty ugly! Also...there some (fairly attractive) insulation pillows that you can put into the recess area of your roof vents/fantastic fan (another large heat loss area.
For the outside. To have a constant water supply...your outside supply faucet must have electrical heat trace (heat traced and insulated to below frost line). We put water hose connections on a pex type plastic line (heated and insulated) to our camper. Not a must, but helpful would be skirting! You can have custom made, snap-on type vinyl skirting made for your unit at a fairLynn reasonable price (though it will probably be a grand or more). When your ready to relocate, unsnap, roll it up, put it in the basement and ?hit the road?! If you are going to stay in one spot for an extended time, a small (50 to 200 or so gallon) propane tank could be rented and tied into your system. We have a 50 gallon tank that we bring with us when winter boondocking....as we are right now. It was 10 F when we left camp and headed up the mountain this morning (typing this via my wife?s smartphone, we have reception here at about 7300 feet)!