That's how I started out for winter coverings for my run five years ago. It only took the first fierce winter wind, and I had everything blow up like sails on a boat on the high seas. Then I got some 2x4s and stapled the bottoms to them to hold the plastic sheeting down. It worked better, but by winter's end, the plastic was slit and in tatters from shoveling snow around the pen.
Then I got the idea of stapling plastic onto light wood frames, 3'x 6' and wiring them to the pen sides. This has proved very effective, easy to take down and put up and durable. I still use these on one wing of my run.
But the very best solution was to use some double-walled, light weight plastic green-house panels someone gave me. I cut them to fit the new run I built last fall, secured them in place with 1/2"x1" strips of wood screwed to the framing. Unlike plastic sheeting, these should last for years. And they insulate so well against freezing temps, it was a full ten degrees warmer today in the pen during a snow storm. That's without the sun shining.
I was brainstorming to also find ways to keep out the wind and snow out of the run and found this link on you tube which I'm going to try. Right now using plywood and tarp. This idea keeps it warmer and dry plus easier to store. Similar to the plastic curtains but not as time consuming to put up and take down in Spring. Although its for a porch it can be used on a run with wood or could even tie onto wire.
Do the chickens stay in the run area at night or are they locked into a coop? I'm looking for a secure run that the chickens can stay in and noticed your hardware cloth only goes up partway--if they stay there at night have you had any security problems? Thanks!