If the trailer is steel, I wouldn't cover it. The cover will abrade against the trailer in the wind and can rub the paint off down to bare metal. Depending upon the fabric, you can also get condensation under the cover and promote rust development. If it's not a UV product like Sunbrella, it's going to break down quickly in the sun and wind and you will probably get no more than 2 years out of it. I would put tire covers on or just cut a piece of plywood down to slip into the tire wells to prevent sidewall damage from the sun.
Parking inside is always nice but you need a pretty tall building.
I bought a tent-like structure from Shelter Logic. We have brutal winters here & it's held up well.
I got one with a front & back opening so I can drive the trailer straight through as it is a close fit until it's in.
I did make the mistake of not considering the curvature of the tent so I ended up mounting it on railroad ties. It still works well.
I had used a trailer cover ages ago on my previous trailer, it deterioted in the elements (the cover, not the trailer). When I bought a brand new trailer 2 years ago, I parked in the shop, but this winter, my trailer was regalled to outdoors and as someone (hubby) bought a brand new bobcat & thought that deserved to be undercover more so, he is right, is costed waaaaaay more. I chose not to cover it as I did not want that plastic near my trailer and the mess it made when it broke down & blew everywhere.