A few things about this subject. In reference to head position, a low head = a calm horse, it's a grazing or napping positions. A high head = an alert horse, looking for potential danger.
Yawns = stress, it's a way of releasing stress, but it means the horse is/was just stressed. Repeated yawning = very stressed or sick (physical stress). IME.
It's interesting CA's experiment it shows two things, horses don't like loud noise, and horses learn from release of pressure - that's all really though. When his head was up 'pressure was on' with the noises the horse didn't like. When his head was down it relieved the pressure. Unless he put a cue to this act I don't see it helping much, unless he hopes the horse will keep his head down for the rest of his life?
"Put your head down" is a cue I teach every horse. You can do this many ways - CA's crowd noise clearly worked, but you could also just use pressure on their poll (by pulling straight down on a lead rope) releasing pressure when they move their head down or (what I use) Clicker training. But however you teach it the cue "put your head down" teaches them to do just that. This skill does more than make their nose closer to the ground, it helps horses 'shift out of flight mode'.
I am working with an Arabian mare who's been mildly handled for the 23 years of her life so far. She leads and is relatively easy to handle - but does no form of work and is never expected to do much, after kicking her owner 3 times no one besides me and her owner can handle her - each kicking incident was out of fear (clear fear, like a plastic bag rattling that spooked her and such). She has no aggression in her, but her fear takes her over more than she can control herself.
I recently started working with her with Clicker Training, just for fun to keep her mind busy. First I taught her that when I don't ask anything of her her nose should be down. So when I'm not doing anything, her mind is in 'neutral' - not looking for danger. Now she's learning several other skills including targeting, backing, touching 'scary' things and putting scary things on her back and head. She's progressing faster than I ever imagined. She's gotten to the point where when I present an object that makes her nervous, she puts her head down, if I ask her to touch it, she'll muster up all her courage and touch it. She knows now that I present all sorts of silly things she will be expected to touch, and none have ever hurt her.
She's working up to riding and coming along quite well, faster than any other horse I've worked with - but I'm staying slow making sure every step is solid, with her history I want to be careful.
So point is, teaching the head down skill is great for shifting horses into a calm spot. And Clicker Training works great for nervous horses, it just gives them confidence. :)