Hi shevy,
We have an owner-written
Water Systems Winter Usage Guide that will help you keep the water running.
The tips and techniques in that guide pretty much assume you have shore power available. If you don't, your battery just won't provide enough power to run the furnace, lights, refrigerator, water heater, and other things for very long.
Holding tanks can be a problem. If temps are just a little below freezing, running the furnace should blow enough warm air into the underbelly to keep the holding tanks from freezing. But if temperatures are a lot below freezing, you really need tank heating pads.
Leaving the rig for a few days can be problematic. You'll have to leave the furnace running with the thermostat at a high enough setting to keep everything from freezing. But that implies 1) that you'll have enough propane and 2) that there are no glitches while you're away.