Leave the valve open - there's no reason to shut it. I winterize my TT in the driveway, then move it to back yard with a slightly different tilt. I may not have gotten all of the water out in the drive so I just leave the valve open. Most of them are plastic valves so all it takes is a couple of teaspoons of water to freeze in them and break the valve.
The worst that can happen from an open valve is that you forget to close it when you fill the water tank - so you spill a couple gallons of water.........
I leave the valves open to my gray and black tanks also.
Bill