T@B Outback Ski Chalet

1. Yes. Heater works just fine winterized with the no water method.
2. No because the Alde heat doesn't extend to the plumbing pipes or storage tanks. An extensive mod would be required and it's doubtful you could power it while towing at sub-freezing temps.

There is a thread on here about doing a modification to add heating pads to the exterior tanks, but you would still run into the issue of powering it.  It's worth a look though.

Just dreaming but --

Ideal solution would be a winterized T@B factory option that includes additional insulation and sealing plus a two zone Alde system.
Zone 1 would utilize radiators for the cabin like it works now.
Zone 2 would include heat transfer plates on the tanks and radiant tubing wrapped on all water pipes.
Zones would be managed with circulating glycol from the Alde and a two zone thermostat.
Top this off with a Zone 1 12v fan sucking heat from under driver's side couch and pushing it under wet bath floor into sink cabinet (someone did this mod). Or strategically placed radiant tubing tied to the Zone 2 controller.
Thermostat setting for Zone 1 maintains the cabin heat at whatever temp you want (like digital thermostat works now).
Zone 2 setting monitors the tanks/pipes and keeps them above freezing (automatic if enabled).
One big IF here is a two zone Alde controller that runs glycol through each zone independently. If that were possible you'd have a system that takes care of all your heating requirements plus freeze protection. It would run on shore power continuously as needed or on propane and house battery for X days at a time.
The extra insulation and sealing would support towing at sub-freezing temps.

With RV antifreeze in the black tank you can get a weekend of toilet use out of the Outback no problem.  We just spent 4 days at Whistler using electric hookups but no water.  If it's just one or two nights you don't need a shower.  

I'm tempted to add heat pads and tape underneath, but it might not be worth the trouble.

Agree with @db_cooper - we've done the same multiple times in temperatures dropping into 20ies and camped for 2-3 nights while in fully winterized state (no water hookup, only electricity connected). We bring on board a jug of water to be able to manually flush toilet bowl after use, and we have a separate small water conrainer with a spout for use on the kitchen sink. After we empty black / gray tank at the end of the weekend, we make sure to add RV antifreeze to both via all drains - that usually takes one full gallon of ready-to-use antifreeze. Never had a problem.