Large volume is relative, of course. A cheap 10 gallon, 4ish cfm compressor does fine for me. The tank size is pretty much irrelevant here since it's running basically continually during the process. A massive body shop compressor is not required by an means.
If your RV is set up for cold weather operation, using the water system in below freezing conditions (with the furnace on etc.) is fine; it's designed for that. There is a lot of variation in how well RVs are set up for cold weather use, though, ranging from not well at all (pipe runs exposed underneath, etc.) to reasonably decent (pipe runs and tanks all inside the insulated envelope, maybe tank heaters, double-pane windows, etc.) Obviously without heat any RV will freeze eventually if the average ambient temperature is below freezing.