Looks like the dog’s eye has been taken cared for by a vet. See the button method?I would reach and pull any dried poop off, and trim any poopy feathers. I don’t bathe chickens, especially in cold weather. There is no danger of fly strike in winter and as long as she can poop, she will be alright.
I would really check that dog’s eye well for any punctures into the eyeball, and even use a magnifier. We had a terrior with a furry face like that and her eye ruptured after a bite from our other dog. It sealed itself off, and fur stuck to it. When we returned a couple of day’s later we found it right away although our daughter hadn’t noticed it.
It’s a white button. A little hard to see. They sew the eyelid partially shut with a button while you use terramycin for a week or so to heal the corneal wound. It keeps the dog from rubbing the sore eye til it’s raw on the floor and the furniture etc.
cone of shame is the second line of defense.