Buckbeak01
Songster
The coop looks like it has good protection - I would not add any plastic or decrease any of the ventilation. However, adding some cover to the run to help keep it dry could be good. Our first coop was a big dog kennel with perches and tarps on top with mostly open sides. The chickens did fine all winter (central NC). We have additional coops now that offer more protection and shelter, but many still like the big open cage.
I did a bunch of reading/research and proper ventilation was the big take home. There was a coop design in Alaska with an open front to promote ventilation - chickens did fine!
On a side note, my chickens LOVE playing around in the are underneath coops like yours. Have you thought about enclosing that and adding it to the area of your existing run? We let ours free range most of the day, and when they aren't pecking - they are underneath our little coop or the back stairs!
Thanks for the advice! That's funny you mention that. My girls always end up going under the coop to dust themselves when they are out free ranging. It's like it's their "hang out" spot. Lol.