Horses bite, or try to bite, people, too, and sometimes it's about the same things that go on in the horse world, but sometimes it's about other things. Although I have a zero tolerance policy for biting, when a horse bites or tries to bite I try to listen to what the horse may be saying with its bite. Although biting must always be stopped cold, sometimes there's important information in that bite. I've come up with a number of reasons why horses may bite people, not necessarily in order of how often each type of biting occurs:
1. Dominance. I don't have any interest in being treated like another horse. A dominant horse may bite in an attempt to dominate you and make you move away. This may be more subtle, such as nipping, or even careful clothes-nipping. This is a boundary-crossing issue for me - in fact all biting is a boundary issue - it's intruding into my space, so I work on it in terms of that by moving the horse out of my space and making it clear that I set the rules for our interactions. This doesn't mean for me that I'm my horse's "alpha" - I think horses are pretty good at distinguishing between horses and people - I think of it as being my horse's "people" and the rules are different - I don't need to "dominate" my horse to make this work.
2. Play. This is often an issue for young horses, who try to engage you in play as they would another horse. Again, it's all about ground manners and boundaries, and making sure that the horse understands that the "people" rules are different from "horse" rules.
3. Protecting food. A horse that is worried that its food may be taken away, or that has been having trouble getting enough to eat, that has been starved, or that is on a limited diet for some reason, may protect its food. Often, this can be solved by making sure the horse has a protected place to eat and that the horse is getting enough to eat.
4. Horse on horse aggression (where you get in the middle). In my experience, this is one of the most dangerous situations. I am absolutely strict with all the horses - no expressing aggression to another horse when I have you on the lead (when I'm leading a dominant horse), and no aggression towards another (more submissive) horse when I have that horse on the lead. This is also an issue when you're among loose horses - I'm very strict that my space is to be respected and that no one is to show aggression to another horse when I'm around - but I still pay close attention to what's going on around me. And it's not always the more dominant horses that cause issues - a less dominant horse will still sometimes go after an even more submissive horse, particularly if the herd alpha isn't around.
5. Grooming. When you are grooming a horse's neck, withers and back, you may find the horse bending its head around and trying to groom you as it would another horse. Some horses use quite a lot of teeth when they groom. Gently moving the horse's face away is usually sufficient to interrupt this behavior, although if your horse is a gentle groomer, you may decide to permit it.
6. Poor treat-taking manners. A lot of people who feed treats find that their horses become pushy, mug them, and even nip or bite when looking for treats or taking a treat from the hand. I do feed my horses treats, but paradoxically I use treats as a way to teach the horse to respect my space and that I decide how and when they get the treat. I teach my horses to take a step back from me before I step forward to give them the treat, and I also have a hand gesture I use to have the horse move away from me.
7. Pain. This type of biting will occur when you are interacting with the horse in a way that causes the horse pain, and the bite expresses the pain and is telling you to stop. A horse with ulcers will often attempt to bite when being fed, or when being girthed/cinched. Or it just may be that the horse is objecting to abrupt girthing, or that folds of skin are caught in the girth or cinch. Other types of pain, such as muscle, joint or myofascial, or a poorly fitting saddle, can cause pain and biting when saddling or even grooming, and if there is biting associated with bridling the horse may be saying that it has a dental problem, the bit hurts, or that the work you will be doing under saddle is painful. We have one mare at our barn who wants to bite when I blanket her - her blankets don't fit all that well and she may have some chiropractic issues as well - and she and I have a compromise - she can bite the wall or the air, but not me. This works for both of us - she gets to express her opinion and I don't get bitten.
8. Fear. If a horse has been abused by people, it may bite and show other signs of aggression out of fear - it's taking preemptive action to defend itself against anticipated abuse. This behavior may be worse in environments where the horse has experienced abuse - in a confined place like a stall, say, or while tied. Abused horses can be very dangerous, and require careful handling, and sometimes just punishing a horse in this situation can reinforce the fear and the aggressive behavior - it's better if you can interrupt the behavior by changing the conditions and working with the horse to convince it over time that it is now safe.
9. Frustration, impatience or irritation. People put horses into situations - such as standing tied, or having to wait for something to happen - to eat, to go back to the barn or back to the pasture - that lead to frustration or impatience, and some horses will bite at those times (or do other equivalent behaviors such as head-butting) to express their frustration or impatience. People rules apply: no biting, no matter how frustrated you are. But I also try to teach my horses emotional self-control so they can tolerate situations that might make another horse frustrated or impatient - there are a number of exercises for this, such as ground-tying and variations on the "just standing around" exercise.
10. Hormonal or other physiological cause. Some mares get benign ovarian tumors that can cause serious aggression problems, both towards horses and people. There are also other conditions that can cause aggression, including biting. A blood test for hormone levels is a good idea as a starting point for a horse that is persistently aggressive. Stallions can be prone to biting due to their hormones - proper early training is the best medicine for this. And there are other, rarer, physiological or neurological conditions that can cause biting, usually in association with other types of serious aggression.
To deal with biting, it's important to me to establish my personal space, into which the horse isn't to intrude with their body (or teeth). This takes care of a lot of the issues. For others, when you're close to the horse, as when grooming or tacking, the "accidental" pointed finger to the muzzle often does the trick, and in cases of frustration or impatience, some horses actually respond well to praise and rubs for exercising self-control. In most cases, if I'm consistent, biting shouldn't be an issue - but if it is I pay attention and try to figure out what is causing the behavior so I can eliminate the cause if possible and not just control or punish the behavior.