I think I'd winterize it and then just use jugs of water.
If you do a lot of winter camping without hookups I'd also suggest getting a catalytic heater that runs off propane. We used one for more that 16 years and absolutely loved it. In fact, we never used our inefficient RV furnace. The catalytic puts out an even heat to keep you toasty warm. We never slept with it though. Besides, we like sleeping in cold temps!
You mentioned 'alpine forest' - do you mean Alpine, AZ? Pretty place up there but yes, you'll get cold temps. Enjoy!