I would think just turning off the water at the valve and flushing it should be fine. The bigger problem is water in the pipes. And now that its plumbed that way Im not sure how to drain that. Maybe turn off all water to the trailer first, then open valves, relieve pressure, then flush, etc. You could also dump some RV anti-freeze in the toilet before flushing, so the residual water in it wont freeze.
Hopefully the water supply modification is in pex so it can expand a bit. I had two rentals in snow country go vacant one december (well one was an eviction, and I should have thought about it) and since no one was living in either, the heat was off (all utilities) and naturally if got cold enough to freeze and destroy some hard-to-get-to plumbing. So if you are leaving the trailer for the winter in a cold climate, its good to be looking into this now.