The key is to figure out WHY the horse is biting....fear, dominance, pain, or he just plain doesn't like you. Aside from pain (sometimes) it's the person's fault he/she is getting bit. When a horse bites, kicks, etc. it's a direct result of how the horse views the person and how poor the relationship might be. To punish him by smacking, which is a predatory response from the human, is to tell the horse you don't care about how he feels about things and how he views things. The horse can not truly respect/trust you if you do that.
Punishment really doesn't work for horses because they are a prey animal and we are a predator....we think nothing alike. Dogs respond to punishment b/c they are also a predatory species. A lot of the time, what we think we should do, we should actually do the opposite with horses.
When I work with horses who are labeled as biters I first read the situation and assess WHY he is biting, then take the necessary steps to fix it. Set the horse up for success so he never feels the need to bite. If the person does get bitten it's his/her fault for not reading the situation correctly....so if they do get bitten backing cures biting because when you move the horse's feet you are establishing yourself as alpha, and you back him until the look on his face changes. However you are not yelling, you are not aggressive (you are assertive) and you aren't feeling mean or mad...."the attitude of justice is effective."