We have several types of "covered" outdoor arenas out here, there are the ones like what I think you are talking about that look like these http://www.clearspan.com/wcsstore/En...undation_l.jpg
however i've been told the same things you have, they are very difficult to heat, so are freezing in the winter, and since the don't seem to often times have openings, I could see the humidity in the summer really building and making it horribly hot.
There are also what i'd call converted outdoor arenas, that look like these http://www.trusteel.com.au/media/ima...Arena-35-3.jpg
Theres one near me that's a bit less fancy than that one. It was originally like one of those half barns that are open on one side and have a wall on the other. The guy set up a pen around the open part and then secured metal panels to block out the wind, but left it open at the top, this way it vents in the summer, however I couldn't see you being able to heat it.
And then there would be one like this http://www.whiteleafproperties.com/1...ered_arena.JPG
Just add some fencing and a gate around the edge. It would vent and be nice and breezy in the summer, but again wouldn't heat.
I don't know enough about the first one I listed to know if you can heat it or not. I'm sure someone else has more experience and would be able to tell you. If you know anyone in your arena with the kind of arena you are thinking of you could go ask them things like how much it cost to make and what company you used. I'm sure on of your local tack shops might have an idea ask well. Covered outdoor arenas are really nice IMO because they keep out the wind, rain and snow, but are cold still, even if they cut down the wind but are very very nice in the summer cause of how airy they can be.