Just my view on storage.
Unless you are worried about someone stealing them. In a cold climate, where winter temps are consistently below freezing, the best place for your battery is in its battery box on your trailer. Before putting into storage, fully charge it, if needed, add distilled water to fill, and disconnect the negative terminal. A fully charged battery will not freeze until temps are somewhere below -50° F. The colder it gets, the slower a lead/acid battery self discharges. According to the US Army COE:
"Batteries should be stored in a cold place, say, about -l5°C, Storage although when fully charged to a specific gravity of 1.280 or greater they can be stored at -1°c indefinitely without deteriorating."
My reading seems to indicate that the expected life of an RV cover is about 3 years. They are somewhat expensive and hard to install and remove. A tarp is a bad idea - they trap moisture and cause more problems than they solve. RV's are designed to be out in the elements. I close mine up, and set the tongue jack with about 2 degrees of tilt. I think I'm more likely to break something by walking on the roof while it is covered in snow than any problem caused by the snow. This assumes you have kept up on keeping the roof properly sealed.
Tires should be clean and to best ability, kept dry. I store in a field and drive up on some 2x10 with a set of plastic cutting boards under each tire (wood can hold moisture). Tires are inflated to max load pressure. I have read, but have no proof, that it is not advised to store tires in contact with cement, supposedly the lime content can degrade the rubber. But on the other hand, my belief is that trailer tires should be replaced every 3-5 years regardless of mileage or how "good" they look. It is a good idea to cover tires exposed to direct sunlight while stored for extended periods.
Good luck and safe travels. Enjoy your new trailer.
I am starting to think, that I will never be old enough--------to know better.
Tolerance will reach such a level that intelligent people will be banned from thinking so as not to offend the imbeciles. Fyodor Mikhailovich Dostoevsky, Russian Novelist
S.E. Mich. Flagstaff 26FKWS / 2022 F-150 3.5 EcoBoost SCrew Propride