Mud for coop floor?!

[x3Silksx3]

For a long time now I have dirt for the ground, Now I want to keep my silkie's clean but it rains a lot and they try to find bugs getting them selves incredibly dirty on their face!!! I don't know what to do, I always change out my coop with hay but it keeps getting muddy and rotten! I have no roof to my coop, it was built a lonnngg time ago, i'm taking in consideration of building a new coop with a roof, the coop I have now has a BIG tree towering over them, its getting old, So worried it could fall!!! Anyways, I honestly don't know what to do...

 

[sunflour]

IMO if you have the space and resources to build a new coop/run with a roof that would be the way to go. I would be worried about the old tree and the damage it may bring. And it would be impossible to remove a large tree hovering over the coop.