TBH, I wouldn't worry too much about this. It is after all how a horse would get all his nutrients if he were wild. Ours love eating leaves and branches off our ash tree, so much so they will pick at it giraffe like. We also have a spring in the field and they like licking the mud around that. They have a mineral lick too, and get some hard feed with minerals etc in.
I would either feed some minerals in their hard feed, or try and mineral lick. Horses eat the long coarse grasses to help clean their teeth, so eating the wood could also be his way of doing this.