Oh boy, if my horse bit me he would be disciplined but good and I don't care if he/she was "playing" or not. These are NOT children. (human) You can NOT reason with them. Watch herd dynamics. They don't play around when disciplining! If my horse was to do a large transgression (such as biting) they would get a pretty good pop on the nose and I would become the crazy lady screaming and waving my arms. Believe me, their feet would move. The yelling and moving of arms should last 10-15 seconds. The trick is to move the feet. In a herd the one who can get the others feet to move is the boss, (or at least higher in the pecking order.)
Small transgressions will start with a voice growl. Most likely a "stop it!" If it continues, (as in immediately continues, not the next day continues) then the discipline gets stronger until he/she stops the behavior. (like CA says as easy as possible, as strong as necessary)(I'm paraphrasing here)
I have to disagree with Dave here. It shouldn't matter if the horse is bored, young, whatever. There are some transgressions that should NOT be tolerated. I can feed any of my horses (I have 23) by hand and they WILL NOT bite me. (or anyone else)
I do believe in positive bonding. I also believe in positive reinforcement. BUT, not with dangerous behavior. (that little nip can turn into a dangerous bite real quick if you're not careful) My horses are NOT afraid of me. But they DO respect me.
If you read what Sparky said,she said, if they try to bite to do this, if they actually bite do that, well, I'm sorry, but it shouldn't get to the actually bite. If they even try, they get the crazy lady and usually don't ever try again.
If you notice (or re-read) what I said earlier, I am not beating my horses continuely. (or ever) It is mostly in the attitude that you portray. You must have the attitude that you are the boss and expect them to behave accordingly.