I have seen deer eat the bolls. Watched 20 popping them in their mouth. However the place we were hunting was infested. Most places I hunt they don't eat the cotton.
But they will be down in it like crazy. Buddy killed a nice 10 picking cotton last yr. Picker didn't convince him to run. .50 cal muzzle loader made sure he wouldn't. He sees deer bedded in it every season.