You could push them down a bit and let the cows eat them in moderation. You could also dry them out and make corn husk dolls to sell on Etsy or at the farmers market.
They're great for composting because they allow air pockets to sneak in, which aids in the decomposition process. My wife makes corn husk mats out of them. I've tried to make them too, but I guess my fingers are too fat because I end up breaking the husks before I can weave them together.
Husk mats sound very interesting. I might have to look into that. I'm pretty crafty so I bet I could figure it out. I tried the dolls, they didn't turn out well.