They should be fine. I have only seen Oat Hay on sale for pets, but I would be surprised if wheat hay or barley hay is any different.
That said, while I do buy Oat Hay from time to time, I look at it as more of a treat and plaything than a food. Natasha (and Scone before her) will eat the undeveloped seed heads, and then dig in the rest to make sure she hadn't missed any. Once the hay has been harvested, as it were, she loses interest in it, so most of the stalks are just wasted.