That's why I LOVE my dutch doors. When the horse's are alone in the barn, they can hang their heads out and such. My doors are situated in a way that they cannot reach each other. All doors are on the left side of the stall so there is no chance of biting or harassing between horses. It's great!
They are solid wood on bottom, and then the top is a gate, that can be flipped down, to allow the horse to hang its head out, or flipped up and latched to allow for a solid door. However the top part is not solid, its metal w bars.
We used HiQual products when we built are barn, they are durable, relatively good priced, and very efficient products.