I just leave the feathers be. They blow away, get caught in the brush, get eaten, or get mixed in the litter. I've also found chicken feathers incorporated into the nests of wild songbirds in the trees and shrubs around my property.
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So you brought up moisture. Here in AZ it's pretty dry would I help by wetting litter when I add to it? Eventually we will get some rain and then the litter will hold moisture.