Just found this thread and, even though it may be a bit cold, just wanted to add my take on the good advice you've already received.
Dominance and established pecking orders among horses is something that we, as owners, riders and trainers, by necessity, must intervene in to achieve success in our day-to-day relationship with them. But our place in that niche is species-specific. Although we may understand and mimic the non-verbal language of the horse to communicate with them, at the end of the day we are still friendly predators in their midst. We do not look or smell like other horses. And even after thousands of years of domestication, the horse's ancestral memory recognizes that other creatures with eyes on the front of their heads and extended fingers that look like claws have a proclivity toward killing and eating them. Knowing this, it becomes easier to understand how the line between what motivates a horse to exhibit aggressive behavior within the HERD and seemingly similar behavior toward HUMANS becomes blurred.
The primary instinct a wild or domestic horse is preoccupied with 24/7 is it's survival. Subordinate instincts to survival are procreation and fear (flight or fight). All horse behaviors are exhibited characteristics within those instincts. Hierarchy and dominance are in the procreation sub-group; the strongest and smartest are herd leaders and the first in line to reproduce. It also establishes order and cooperation within the herd. And flight is the first response to the fear instinct, followed by the last resort of fighting if the flight route becomes exhausted or eliminated. (That's why a ROUND pen works. Unrestrained flight. No corners to become trapped in.) Since we are definitely not directly involved with the procreation instinct (excluding controlled breeding, of course), virtually every response we intentionally or unintentionally elicit from the horse is a manipulation of some aspect of the fear instinct. Adding the extremely tractable nature of the horse (their innate response to demonstrated leadership), by controlling the fear instinct and providing leadership by imitating their hierarchy and dominance characteristics we domesticate and train horses.
The blurry line comes when WE cross over into believing the horse has accepted us as another more dominant horse and start assuming aggressive behavior toward us is a challenge to our dominance. In most (but not all) such exhibitions it really comes from reaching the horse's fear instinct tipping point. And in most cases it will happen when the horse is confined or restrained, eliminating it's first preference to flee and leaving it to resort to a fight. Even a horse that may occasionally turn to confront you in the round pen is reacting from fear and not motivated by a desire for dominance. Sending them off or driving them away initially forces even the tamest horse into the flight mode, an inherent fear instinct response. If you get out of position (drift forward of the girth line) the "escape route" is cut off and the horse may either reverse direction or switch to the fight mode. And sometimes a horse may quickly learn there is no escape in the round pen and go immediately to a confrontation. It's not for the faint-of-heart but you have to be persistent, get behind them and initiate the flight mode again. Some other exceptions for going into the fight mode seem to be stallion behavior (for reasons I hope are obvious) and mares in heat. Minus a strong fear instinct around humans, when the procreation instinct takes over it's a very bad place to find yourself on or between horses consumed with a primal response.
Another example of a fear response usually misinterpreted as a show of aggression or obstinacy is asking the horse to do something it doesn't understand or continually asking for something it DOES know but in a way it doesn't understand. New learning pushes a horse to the edge of it's comfort zone. And when a horse becomes confused or loses confidence in the leadership, it's on a banana peel straight to the fear instinct flight or fight response. Working with thoroughly broke or normally passive horses can often lull us into a skewed understanding of these instinctive responses, too. But it's all really a delicate balancing act that is extremely important to understand. Especially with youngsters and horses in early training. Trying to immediately overpower a fear response with anger, punishment or enforced restraint can be entirely counter-productive. It only reinforces the horse's reaction by providing additional and escalating frightful elements to the experience. To me, it provides the opportunity to create a calm and quiet learning experience on another day. Of course pain, lameness, illness, ill-fitting tack, etc., can also be contributing factors to behavioral responses. But even those situations knock on the door of the horse's fear instinct.
Even issues of pushing, crowding and biting human handlers are related to the horse's fear instinct. Or more specifically, a gradual diminishing that leads to a lack of it. Familiarity breeds contempt. Such horses need to be "reminded" we are still predators and require respect to keep us on a friendly basis. And that's accomplished through various reprimands that re-acquaint them with the necessity to keep a respectful eye on us but not to a level that interferes with trust.
Truly understanding why and how horses respond to stimuli in their environment is the Mother's Milk of successful horse training. Armed with that knowledge you can create effective training techniques on your own to get almost any response you can imagine. Not all horses are exactly alike. So the more ways you learn or create to accomplish a desired result, the more successful you will be. But keep in mind there may be 5-10% of the horse population that seem to defy everything we've grown to understand about them over the past 5,000 years. Learning to recognize them is a real measure of horsemanship. Even so, having an opportunity for up to a 90% training success rate should be a very strong motivation to want to really know what makes most horses tick. ~FH

"Abuse is when a human action or reaction is obviously accompanied by anger, rage or adrenaline. Proper correction and reprimand are done in silence with thoughtful intent. Your horse knows the difference." ~FloridaHorseman