We bulit our coop and run last spring. We used wire over the top of the run... Well, after a few months of rain, ice, snow, sleet, hail etc... I was wishing I had built the roof solid.. We did place a tarp over it and one side to block the wind some , before our first windstorm (50+ mile winds) and the girls have really enjoyed it..  We will be covering it, this spring, w/ premament roof.. When we build my new coop it will have both a roofed area run and a wire covered run...  
Good luck..Dixie