Here's another idea as long as we're dreaming - I used to ride at a barn that had a covered riding arena connected to the barn by a covered walkway. It was GREAT - didn't matter if it rained or snowed, plenty of lights mounted in the roof so you could ride all night if you had a mind to. The standard covered arena around here is a metal frame building without the skin. Sorta like this, without the barrels!
Instead of the fence sections, my old barn had a wooden wall built up about to the height of your shoulder when you were on horseback. Stopped drafts and rain blowing in.
Yeow, I'd kill for that arena.
That's a great arena.... here, sometimes they add walls on the three weather-facing walls only or half-walls.
I want to have a small completely indoor and protected arena, and plenty of outdoor space for a large arena, dressage arena, jumps, and a round pen. That would be likely uncovered, but we'll see ;~D