I'm going to post an answer here, even though I don't have a horse!
I work with a llama rescue organization that deals with a fair amount of "behaviorally-challenged" llamas, and it sounds like some of the behaviors are very similar to what you're describing with horses.
Like horses, llamas are herd animals. Although much smaller than horses (weight-wise, anyway - the largest llamas weigh between 400-500 lbs), llamas are "semi domesticated" meaning they have not been domesticated as long as horses. A wild llama will not get close to a human. They have many of the same behaviors - respecting another animals' space indicates respecting their standing in the herd - a subordinate llama will not get in the space of a dominant animal, but a dominant llama can enter a subordinate llama's space. A llama that is mad or not liking something will pin it's ears back. A llama that stares at you directly in the eyes with its ears back is challenging you.
With llamas, most of the problem comes from animals that are over-handled when they are babies (crias). We have a term for these animals, ABS - Aberrant Behavior Syndrome. In most species it is called imprinting - the animal imprints on humans and never develops a fear of them. The worst offenders are usually bottle-fed, usually males are worse, but females can be terribly dangerous as well. A bottle-fed llama is the most wonderful, adorable docile pet . . . until it reaches maturity. Even if it's gelded, which does help, it will treat humans like another llama, meaning that it wants to establish dominance in the herd. They do this by charging, chest-butting, stomping with the front feet, sometimes by biting. I don't think there are any cases of humans being killed in the U.S. but a llama can certainly send someone to the hospital. Usually these animals are more likely to go after smaller people (women), and most will launch their attack when the person's back is turned. These llamas only make up a small percentage of llamas. Fortunately MOST (but not all) llama and alpaca breeders are becoming more aware of this syndrome and take steps to prevent over-handling their crias.
Even if it's not bottle fed, a llama needs to know it's place with humans. Because many people who get llamas are new to owning livestock, they can have a hard time training the animals. As you know training a prey animal is different in many ways than training a predator (dog). So sometimes llamas never lose their fear of humans and sometimes they never know their place.
With my llamas, I don't allow them to enter my space unless I invite them. Llamas greet by smelling your nose - I permit this but I don't allow them to push on me, or rub their faces on me, unless I KNOW that particular animal will not try to go the "next step". Llamas that chew on shoes or clothes are trying to see if they can push it to the next step. Some reach a point and never go farther, but I've seen it escalate - quickly- to rearing, chest-butting, etc. You think some of those cozy little behaviors are cute until they are full-blown challenges.
I imagine some of it is also attitude - the animals know if you are afraid of them, and will be more likely to try to establish dominance. I take care of two imprinted white-tailed deer where I work (a science center) - I established dominance years ago and they don't even think about attacking me, but anytime one of my coworkers goes near the enclosure, or a new volunteer usually female - the deer go nuts.
So to make a long-story short, I agree with welsummerchicks that it depends on the animal. Some animals only do the nosing stuff, but some will keep pushing the envelop. I imagine that horses are like llamas - an older animal is probably much less like to try to keep pushing the behavior to next step, but a young animal that is reaching maturity is trying to establish it's place (much like humans). I think the animal can learn - okay the human allows me to rub my head on them, but if I try to bite I get reprimanded. Just like in children, you have to be consistent. If you allow biting one time but not another it's confusing.
Hope this helps!
