Some backyard birds incorporate hair in their nests. In fact, my wife and daughter watched a tufted titmouse pluck hair from one of our sleeping bird dogs. This is a form of kleptotrichy.
If you want to do something to help your feathered neighbors other than provide them with food, water and cover, try offering them nesting material.
Recently my wife and I packed hair my wife trimmed from out little housedog into a wire suet feeder. They next day after we hung the wire feeder up in your backyard, the hair began disappearing. Since we have not caught any bird in the act of plucking hair from the feeder, we have are not sure what birds are using it. Perhaps it is a tufted titmouse, who knows?
If you do try offering your backyard birds hair trimmed from your family dog, make sure that it is free of flea and tick control chemicals and shampoos.
We have a very old blanket on the glider on the front porch. A titmouse has been collecting fibers from it for about a week. There are holes in the blanket where the bird has pulled the fibers out. So glad that old thing is of use to someone.