My horses do it too. I do not think it was because something is missing in diet as well as they always have enough hay to munch on and pretty big place, so I didn't notice the boredom. I noticed though, that they eat up the tulip tree. I mean EAT UP (through the bark all way in). They also LOVE the tulip tree's flowers, so when we have blooming season they spend hours under that tree picking up the smallest pieces (my mom says they are sweet, but I never felt like trying one myself). They also like leaves from it, but not that much. So... May be your horses just like the taste.
I was mean though, so when they started on trees we wrapped all trees with the chicken net for prevention. :)