So far in my fairly mild climate, (Pacific Northwest) I've found the biggest benefit to placing a hive under some kind of cover, helps the hives finish stay looking great. No constant moisture all over the hive.
Here is a pic of a bench I built when I first got bees. I was able to drop the sides down in extreme weather to somewhat protect the hives. Roll up the plastic in better weather for accessibility. Just be sure the top is open enough the bees don't get trapped there. They are kind of dumb that way.
(The galvanized top you see on the bench was an old security window screen from Joint Base Lewis McChord, demo'd many years ago. I snagged up about ten of these 4' x 14' (tables as I use them) and love them! I like the old stuff, besides being made very well, it has a local history)
Here is a larger bench using the cattle panels for the roof support for the plastic. I had to make this myself and after a bit of thought used the ratchet straps to put a bow in the panels and heavy zip ties to hold them in a bow.
(I salvaged these brackets and pipe years ago from a commercial job site. It use to be a laundromat . My husband gets on me for being a pack rat..I stored these for about 10 years before I figured out what to use them for. Hee hee-)
With plastic on, this bench works really great. The plastic was A little ugly though. It did not lay flat because I left a few inches of pipe sticking up beyond the roof panel.
I've since rebuilt the bench-The 1 1/4 galvanized pipe was not strong enough to hold the weight of fall hives. Built a simple 2x8 pressure treated frame to hold the plywood. It rests on the concrete bricks right on the ground
Here is one of my larger greenhouses. You see the bench on the end? I placed hives there last fall, but the buggers just flew up to the top if the greenhouse and the enclosed south side and got caught. Even with the huge open ends.One of the reasons I lost a lot of hives last winter..I lost too many bees in this location, before I moved them back outside.
To have them under cover, you really need a dark building with no windows. They can find the only light to the outdoors and orient just fine.
Using a greenhouse or clear plastic is very tempting for the solar gain benefit. But beware, it is quite tricky to do. Once you see how the bees navigate-or their lack of navigating skills, you should be able to pull it off.