As an oral behavior, chewing or cribbing may be related to horses receiving high grain, low forage diets. Wood chewing may also be reduced by changing the horse’s housing and diet so it gets more forage and more time out of the stall. The pony may just be bored. To add more fiber to the diet feed more hay. It is recommended that the diet contain no less than 1% of body weight of a roughage source (e.g. hay, pasture, etc.). For example, an 1100 pound horse requires at least 11 pounds of roughage (1100 x 0.01 = 11). It is also important not to overfeed grain to horses because this can also result in digestive upset (i.e. colic or wood chewing). With your pony you may want to feed an all hay diet (2% of his body weight).
You are very lucky that you noticed the problem. Your vet wants you to provide enough water to help clean out the horse's system. Follow your vets directions and "Keep them fenced out of the trees."