First, in freezing weather, it is always best to use the fresh water tank and 12v pump in case the CG water supply freezes up at night. Second, if the drain valves are enclosed, then you can leave them closed. But if they are exposed, then leave them open, even the black valve.
We have been in our fiver with temps in the 20s for several days w/o problems. And that is when using electric heaters rather than the furnace. In fact on my last Cruiser, I sealed the furnace duct to the basement. In my opinion, the amount of heat supplied to the basement via the heating duct is insufficient to prevent freezing. "Insulation" used in the basement is usually Reflectix foil, it doesn't really insulate, but reflects heat and is located below the tanks. Meanwhile the I-beams conduct lots of heat out of the basement and have significant holes in them for the slide outs mechanisms. The basement heat duct is located near the center of the trailer and provides little heat around the perimeter of the basement to offset heat loss at the I-beams. With a strong norther, it will have no benefit on the upwind side of the trailer. The tanks are not likely to freeze, they are either empty or in the case of the fresh water tank, carrying lots of water. What is most likely to freeze is the fresh water pickup tube, it is small in diameter, right up against the I-beam and many times located in the back corner of the trailer, far away from the basement heat duct.
If freeze protection is critical, then electrically heated tanks and lines is really a much better answer.
Texas Baptist Men-Retiree Builders member since '01
13 Silverado 3500HD D/A, 2wd CCSB srw, custom RKI bed
11 Cruiser CF32MK