I was thinking the same thing as protégé above. In the event staging business that's called a kabuki drop. It's a one time use prop (per show) with a manual reset cycle. Often the whole thing comes down to the floor to be rolled, then hoisted up on a simple pulley sort of rig. (or attached to a truss and raised with chain motors). It could also be folded back and forth like the old pinfeed paper for a faster drop with no rotational force to deal with. The release mechanism consists of a handful of cords that wraps under the stored fabric attached to a solenoid, sometimes (less common) an electromagnet catch. when you push the button, it releases the solenoid and it drops. There's usually a second solenoid release mechanism that releases the fabric from the top batten to let it come down just as fast as it was deployed.
When you google kabuki drops you'll mostly find descriptions for mechanisms for the dropping the curtain to the floor, the second stage of the apparatus I described above. But the same systems are used for the first stage as well, just with the retention cord/straps instead of the top batten.
For material selection, you'll want to look into "blow thru" materials. This is a product we use a lot for this type of job. http://www.ultraflexx.com/product/speaker-mesh/ instead of a solid piece with u holes as you're describing, this is a mesh, more like a window screen. It's much more uniform than something with holes in it. This particular fabric will let 70% of the wind pass right thru it while still doing a good job as a visual for a screen. It's PVC coated polyester and thus will not soak up moisture. That doesn't mean it's not heavy. It just means it doesn't get much heavier when wet than when dry.
In this application, I'd stay away from motors to deploy the screen. Anything strong enough is going to be way too slow to be useful in a production. You can certainly use chain motors to lift the rig before the show. (or even HF winches if you want to be cheap, but they don't make any strong enough to be safe anyhow) But they won't be anything near fast enough for the effect you want. Any motor that's fast enough won't take much abuse from the wind or weight, or it will cost a fortune.