All very good advice! I'll only add that on the lead , you can almost feel just prior to the horse stopping and dropping its head, so I just keep walking and set my hand so if it goes to drop it runs into the end of whatever slack there is and gets bumped. While I didn't bump them , they learn they did it to themselves.
Under saddle, same thing , forward movement, set my hands, they'll bump themselves. Of course some of our trails are narrow and there is a smorgashborg of delicious leaves! Let's say T moves her head to the right to snatch some leaves, all I do is set the left rein, and move her forward. She learnt quick that not only did she not get her snack, she had to move out a bit more! Being a horse who likes to conserve her energy,haha, she was a fast learner.
Walka, never allowed him the opportunity to develop these habits, so haven't had to deal with it with him.