There are very few places that rent enclosed trailers. If you were in SoCal I have a friend who owns six and does just that, rent them.
If it were me I would contact your local places that sell trailers and ask if they know anyone who rents. They will probably get something for the referral. As far as someone letting you borrow a trailer it's highly unlikely. I have two friends I let borrow mine and that's it. Others have asked and I then refer them to my buddy who rents...and I get 20 bucks for the referral.