Hey scrapdaddy, we're there as well. We have two on trailers and they are adapted for quick response with quick-connects directly to transfer switches. The transfer switches on the houses have built-in females, and the trailers have 50ft dropcords with male ends. These generators are in enclosed storage but in an emergency situation we can pull them out and go to where the outage has occurred. The quick connects are permanently attached to the transfer switch panels, ie the generator is pulled to where the problem is, attached to the female connector, generator started, then hope and pray everything works as intended. My biggest concern is that if it fails at the mother-in-law's house, I'm in deep dookey.
Regarding your thought about enclosing the whole trailer, every man walks a different path, and it's not my place to tell someone else how to store their generator. This is what works for us, and hopefully you might be able to adapt what we have done to your personal situation. A portable generator is a great thing to have, and mobility is a +++++. If you are talking about putting panels around the generator on the trailer, it could work, providing you are able to put a roof over it and find panels that will work for your dimensions, plus be easily removable when operating. Interesting thought!