For two reasons it is best to not let a horse while on a trial ride. First, there are certain toxic plants that can harm a horse and second, it best to keep a horse concentrating on his job and if he were to reach out and try to brag a tree limb or shrub it could cause an accident. If were to take a break or you were at the end of a ride and were near a good pasture it would be OK for your horse to drop his head and graze a little. It is important for your horse to know his job and for him to reach out and try to eat while you are riding is not good. If your horses tries to do this, put him into a little jog and he will eventually understand you will not alow him to do this.