I personally do my roof work in the Spring when I "open it up".
As for the cover, I put one on mine. Does it help things, I think so, but have no real data to prove it.
Have had three motorhomes and we have our first trailer for the second season now.
Luckily we don't have to seal it up till late October usually.
I take the battery out and bring it in the heated garage and trickle charge it every month or so.
I personally worry more about mice than anything over the winter. I take a couple of hours to TRY and make sure I have every opening sealed up to keep them out.
We get plenty of mice in the house in the fall, so I know they want in the trailer also.
Last year (banging on all the wood I see) we didn't get any in the trailer.
Duct tape is my friend. LOL
2015 32 Foot Rockwood 8289WS 5th Wheel
2017 GMC 3/4 Ton TV