I didn't winterize in my OLD trailer. I did however, drain the water heater and empty the tanks.
I had to replace a section of pipe underneath the kitchen sink (CPVC). Pretty easy.
It cracked the toilet valve. Since the toilet was old and the part was no longer available, I ended up having to replace the toilet. That was $180ish.
Replacing the toilet was a good thing, since the vacuum breaker had been bypassed.
Fortunately, I no longer have that trailer...
If the tanks were emptyish, they'll likely be fine.
The nice thing about a demand pump is you know when you have a leak. The pump will run mysteriously = problems!