First of all, biting is normal behavior between horses. If you watch horses play together, they often nip at each other, and buddies mutually groom each other with their teeth along their withers and back. When fighting, horses use kicking and biting to assert their dominance over each other, often inflicting serious wounds. You need to teach your horse, in no uncertain terms, that you are top on the pecking order when it comes to biting and that YOU make the rules. No biting, nipping, nuzzling of any kind period.
Teething has nothing to do with a horse biting people.
When I am handling a horse that likes to nip or bite, I do one of two things. Each time a horse like that comes at me with his nose, whether is seems like a sweet nuzzle or not, he gets a nose massage. Pretty soon, horses learn that they don't have to be so nosey - it is that simple. By the way, while nuzzling is sweet, it often leads to nipping and then biting, so if you let your horse nuzzle you or your pockets, be aware of the danger. Also, be aware that feeding treats from your hand often leads to nipping and biting.