Our 23' has heaters in the gray, black and fresh tanks. They run on
12v, batteries will last about 3 hours, the owner's manual says. While traveling, the TV would provide some power to them, but when we travel I always dump the holding tanks before leaving a campsite and then add some RV anti-freeze to them. That way I don't have to worry about them or running the batteries down.
For the toilet, like others, we carry RV anti-freeze for flushing. Mostly, we depend on rest areas and Cracker Barrel rest rooms, rest areas being the best since they have dedicated cleaning staff.
For fresh water we just buy gallons of water for drinking, don't use the fresh water tank. A little residual water in any of the tanks won't be a problem for them, but pipes can freeze. It's best not to use the plumbing if you can avoid it. If you have room for a small compressor you could blow out the lines before moving on to the next stop.
I would think that pipes inside the trailer would be OK for travel unless you're in extreme cold or very long trips. You could also keep the furnace running.