All you really need is Consistency
I never call a horse finished. To me you finish reading a book, or you finish the work week. I consider all horses to be works in progress, just like a nice lawn they have to constantly be maintained. Consistency is key in having a happy equine relationship. Horses see everything as absolute. So if you allow your horse to eat grass while on the halter, every time they see some grass they will be trying to eat it even when you don't want them too. Sometimes does not exist in the horse world, it is the same as always.
For example let's say that your Grandmother always keeps a full cookie jar, so every time you visit her you're going to go get a cookie. Now one day you go to visit and when you check the cookie jar you find crumbs instead of cookies. You have grown to expect cookies so even though they are none today the next time you go to visit you are going to check the cookie jar, and will probably check several more times afterwords until you are absolutely certain that there will be no more cookies.
Horses work they same way. The best trained horse in the world will turn rotten if allowed too, and the worst horse can become a joy to handle. For example if you are riding and you ask your horse to trot and then he breaks down to a walk and you allow him to walk for 15 steps before telling him to trot then the horse learned that they can stop trotting and walk for 14 steps before being corrected and he will probably try and do it again.
Horses learn through cause and effect. The horse touches the electric fence, the fence shocks him and the horse learns that touching the fence hurts. A colt gets too full of himself and bites the old mare, and old mare bites or kicks him, so the colt learns that you should not bite old mares.
A nippy colt can easily be fixed by lightly bopping him on the nose every time he tries to bite. Consistency in the horse world means every time without exception by all people who have contact with the horse no matter the situation. Don't worry if they keep testing you, as the more they have been allowed to do something like biting they longer they will continue to try to do it.
A foal spends the majority of it's life a horse so when dealing with young horses it is important to enforce the same rules that adult horses live by. Most young horses will try to bite, kick, rear, be pushy when leading, etc but all of these behaviors can be quickly put to bed by correcting it the moment that the horse acts out. If the first time a colt tries to bite a person he is met with a light bop on the nose, he will very quickly learn that you don't bite people. Training is consistently making the right behavior easy and the wrong behavior hard.
The sky is the limit as to what you teach your horse, you just have to remember that consistency is key.