chickens getting into my horse hay

We don't even have our barn done or horses here yet but I have a question/problem.

We have 10 Isa brown laying hens. They are in their coop at night but during the day we like to let them free range. Well, yesterday I found 2 of them in the barn sitting on the loose hay (from a bale that broke). I am worried about them trying to nest in there and then pooping on my horse hay.

Is that a problem? (I am assuming we don't want chicken poop ON the horse hay) How do I keep them out?

I would not want them roosting in the horse hay not only because of the p**p but if they have lice, you can get them and I think the horses can too.

Someone may need to correct me on whether or not chicken lice can transfer to horses