I took the teardrop out of storage Saturday. I have it parked down the road at a boat and RV storage lot so we can get both cars in the garage during the winter. I hate scraping ice off windshields.
It came through the winter very well. I took two precautions, a cover and a solar charger.
The cover was a great find. It's the $89 Classic Accessories brand

It worked perfectly for me, it will go at least one more winter, maybe a few more. Some reviews complain these cheap covers tear too easily. So before I put it on I taped 1/4 inch foam pads on every sharp corner and point like the ends of the hurricane hinges and the galley hatch latches. I cut up a nine dollar yoga mat into square 12 inch pads for these corner protectors. I was also careful to snug it down tightly so high winds wouldn't make it flap and billow too much. Because I worried about rain wicking through the cover and laying on the roof, I put a cheap thin plastic drop cloth over the roof and a few inches down the walls, held down with bits of blue tape. Then the cover over everything. Worked great. No sign of moisture inside the trailer anywhere.
When we put it away last November I also added a small and cheap solar battery trickle charger. Ten watts, small enough to fit onto the lid of the tongue box where the battery lives. Just screwed it down onto the lid facing the sky and clamped the leads onto the battery posts. 35 bucks.

I can't prove it really helped. But after a winter standing idle the AGM battery still had most of a full charge. I can't accurately measure the state of charge on my battery. But I looked at how the smart charger behaved when I got it home and connected shore power. The charger always starts with a high amp bulk charge, then kicks down to a constant voltage absorption charge mode . I checked after five minutes and it had already kicked down off bulk charge, so the battery was nearly fully charged after the winter. I'm giving credit to that little solar trickle charger.
Now it's time to fix some peeling paint on the woodwork and start the next round of improvements.