There's a lot of theories out there in the horse world that are used to describe how horses and humans should relate, or do relate - "predator/prey", "herd alpha", etc. etc. In my opinion - and it's only my opinion - most of that stuff is just plain hogwash, and a lot of it is used to justify training methods that to my mind are often questionable, or even worse. Some of it even works, mainly because a lot of things work with horses due to their willingness and try to figure out a way to deal with us. And don't get me started on those who train, and treat, horses as though they're mechanical objects - repetitious ground and lateral flexion work comes to mind. Some of the people who hold these theories - a lot of you may - are well intentioned - but I think the theories sometimes just get in the way. It's our natural human tendency to construct theories and systems, but we have to be careful we don't see what we're thinking rather than what's actually there. The theory that comes closest in my mind to what's really happening with humans and horses, if they're really working together, is Mark Rashid's theory of "passive leadership" where respect from the horse comes from calm leadership provided by the human, but lately I'm not sure any theory is really needed.
Horses are horses and humans are humans, and horses know the difference. I also believe that, although horses aren't humans, they are "persons", with thoughts and feelings, and it's up to us to provide them with calm, confident, caring leadership and always treat them with respect. And they should treat us with respect - but that means it's our responsibility to teach them precisely what we want them to do for us and not leave them guessing. Respect also has nothing to do with dominance or fear, although a lot of people use the term that way. I believe, although of course I'll never know for sure, that horses think of us as an alien species that they have to learn to understand and communicate with, and that we should think of them as the same. I don't think horses "classify" us - their world is one of immediate experience, not theory. Now of course, as we're learning to communicate, we each use "language" that is typical of our own species, but I think it's in the new language we forge together, that is formed between us - the feel and connection - that the real power of communication arises. No theory's needed for that.
One thing I've been working on in me lately is maintaining that soft feel and connection consistently as we work. It's in the changes - the transitions from one gait to another (including to halt and back, which are also gaits), or from bend in one direction to another, or from regular gaits to more extended or collected, or from ground to mounted, where the connection can be lost, assuming it's there to begin with. Dawn and Pie and I all worked on that together (not at the same time - Dawn wouldn't have stood for that!) yesterday, and it felt pretty darn good. The main work was on me, as usual. I have a tendency to be abrupt (many people do, I think) in making changes - taking off/reapplying aids without feel and softness, or shifting position too dramatically, etc.
One exercise that is very good for me - my horses tell me so by responding so well when I do it correctly - is changing the bend with softness and feel - no exaggeration or abruptness. First, I have to get the feel and connection at whatever gait (we've been working in walk and trot) on a circle in one direction. Good up and out focus by me, correct position of body, legs and hand, and good tracking up by the horse. Now . . . change bend. The trick is to get this to flow. I ever so slightly turn my upper body and eyes in the new direction and move my new inside hand every so slightly back towards my hip and my other hand ever so slightly forward. And increase the feel of my new inside leg ever so slightly - almost not at all. If it all happens at once - if we're just "with" each other and doing it together as though we're a horse/human with no gap/space between what I'm doing and what they're doing, the feel on each rein doesn't change at all - the same softness and feel is there with no loss of connection or increase of pressure, and everything else just happens. My horses have been working hard with me on this one, telling me when I've not quite got it - Dawn and Red get fussy and overreactive if I overdo, even slightly, and we lose the feel, and Pie tends to tune me out and get heavy and braced. (A side note on Pie - a lot of people would treat him as dull and ride him that way - I've been guilty of that myself - when in fact he's just as sensitive and responsive as Dawn and Red - his response to overcuing is just different than their responses, but when I'm soft and have feel he responds to that just as well as they do.)
Yesterday, Dawn and Pie and I were really "with" each other as we changed bend - we were soft together and the feel was there. It was pretty darn magical, and I'll take that magic any day.
A very Merry Christmas to you and your horses!