I've never had to take care of a trailer. But you know, one time I unpacked my gear in Spring, ready for use, and I found that I had unfortunately left some supplies caught up inside..... oh my. Never again.
We usually dedicate a couple of days to winterizing in the late Fall. The pipes and water heater get drained, anti-freeze goes in the pipes, we pull the batteries out, and I clean everything and pull out all the linens and rugs to launder. Then we tie a huge tarp down over it. It pays off the next season.