I've had several biters and nippers. Some very NOT-PLEASANT flesh removers!

One thing I've found VERY effective is when they reach out to start nibbling/nipping/open their mouth to bite- to kick them in the shin (cannon bone). Some folks think this is ridiculous but if you try it you'll find that it does work!
For one thing, they can't see you kicking them underneath their head SO they won't get headshy from someone smacking them upside the head lol-

For another thing, if they can see when you're going to give em a whack on the nose/head/neck, a horse will usually become headshy and/or just get quicker at biting and then jerk away.

Kicking their shins, after the 5-6 time, my biting horses would reach out as if to play with my coat, or give me a good ole chomp, and would stop and look down at their feet. It's hilarious! And it works!

Something that John Lyons teaches is you can rub their noses...and keep rubbing...and keep rubbing...and eventually...the horse gets very tired of putting their mouth/nose on you because every time they do, they get their nose rubbed and pulled and messed with...