Winterizing the Black Water Tank

I make certain there is antifreeze in the inlet valve to the toliet.
But as long as the the tank is empty, it shouldn't matter. Recall the issue is water expands, a (nearly) empty tank has lots of room for the waste water to expand

I drain the black tank. I don't put any water in because you probably can't get all the water out, there will be some left.
Add Antifreeze to the tank and toilet.
Sounds like you got it right.

That's exactly what I do.