What you need to do, and what is most economical and the least burdensome to do, really depends a lot on how your particular motorhome is set up and equipped. I'm assuming it's at least somewhat capable of winter operation since you are doing that already, and so has provisions to keep the plumbing systems from freezing when being used in the winter.
If the motorhome is winter capable (and so has the tanks enclosed and heated, the pipes within the insulated space of the RV, etc.), then typically running the furnace ought to be sufficient. Using a space heater is often not as good as it doesn't circulate the heat to the mechanical areas of the RV as well--often there's a bit of duct from the furnace to the wet bay. Some people install fans to circulate air through the ductwork and use a space heater, or put another heater in the wet bay, or rig up some other means of keeping everything warm...what might work really depends on your RV's setup.
Be prepared to use a fair amount of propane keeping things warm. Needless to say, running out would be a real problem. On the whole, I personally think it's preferable to winterize between uses (blowing the lines out with an air compressor rather than pumping antifreeze through them makes that somewhat more palatable to do repeatedly, though it's still a chore) or simply to avoid using the plumbing system when tailgating, but obviously it's your call.
