Like a needle on a gauge, your horse's head position is an indicator of his emotional state. When his head rises, he's tense and prepared for flight; when it lowers, he's relaxed and at ease. By teaching a drop-head response, you can ask your horse to calm down on cue—especially useful if your horse is the nervous or spooky type.
I'll explain how to teach the cue from the ground, then from the saddle. It's straightforward, but does take patience on your part in the beginning.
From the ground. Put your horse in a rope halter with training lead. Place your thumb and index finger on the knot just below your horse's chin and apply gentle, steady pressure downward. You're not trying to pull the head down; you're just applying pressure as a cue. Watch your horse carefully, and the instant he drops his head even a fraction, release the pressure and praise him. (It's better to err on the side of releasing a bit too soon than a bit too late.) Then ask again.
The first few inches down will be a challenge. Be patient and keep at it. Once your horse gets the concept, he'll soon be dropping his head all the way to the ground every time you ask. Eventually, encourage him to keep his head down at ground level for a few minutes, to allow time for him to feel the serenity that naturally comes from a lowered head.
From the saddle. Once your horse responds reliably to the cue from the ground, tack him up (a snaffle bit is best for this) and try it mounted. From a standstill, shorten one rein a bit, lift that hand slightly to apply light pressure to your horse's mouth, then just wait. You'll feel tempted to increase the pressure to get a response—but don't. Apply just enough pressure that your horse begins to look for a way out of it.
Then, the instant he drops his head even slightly, release the rein entirely and praise him lavishly. Don't worry if he moves about a little while you're working on this; just focus on the head dropping and release whenever he complies. As before, the first few inches will be challenging, so be patient. Once your horse figures it out, he'll begin to respond quickly and willingly.
Then practice the drop-head cue frequently on an ongoing basis, especially any time your horse becomes tense or fearful. Eventually, your horse may start dropping his head on his own whenever he begins to feel nervous or anxious, "self-medicating" himself in order to feel calmer. Now that is a result worth working for!
Julie Goodnight, known for her ability to teach horses and riders of all skill levels, hosts "Horse Master with Julie Goodnight" on RFD-TV. She also presents clinics nationwide from her home base near Salida, Colorado (juliegoodnight.com).