it won't hurt them, and they will be really interested if you leave a few corn cobs on them. I half peel the corn and toss it in and the drag it around and scratch the rest of the peels off before eating the corn. they don't eat the husk. if you have goats though, they love husks and stalks.
At the end of corn season, I pull up all the stalks with the under-developed cobs on them and give them to the chickens. They love the cobs, and it gives them something to keep busy with!
Oh yes, we toss corn stalks and cobs for the animals all the time. They even love the cooked ones we've eaten... the chickens will pick off any remaining kernels, and the pig will eat the whole thing.
They love garden clean-up time... yesterday they got overgrown spinach, lettuce and turnips. Today they'll likely get the rest of the corn crop and sunflowers. I've been giving them a little every day to stretch out the fun. They'll clean it all up.