I put thick cardboard and it seemed to help a lot!
Looks like my "old" coop! I use to use tarps but now that I moved I can't since the wind will just tare them up like nothing. The heavy duty metal wood roof blew off once.
I was thinking about the tarps in the inside of the run....maybe that will work.

Here is what my coops looked like during the summer.
View attachment 4274018
Both of our coops look almost the same

You can see how the wind blows around in the run ( I should have made them shorter).