Sometimes this is just a habit that a horse has picked up. The horse I'm leasing is in perfect health, no mouth/teeth issues. At competitions though, she is ridden in a gag bit with shanks, and she likes to lip the shanks. Especially if your holding the reins, she'll grab the shank and pull. Annoying...It can be. I have associated it with her wanting to get out and run, like she's holding in energy and that's her "outlet"
"The greatest pleasure of a dog is that you may make a fool of yourself with
him and not only will he not scold you, but he will make a fool of himself too."