Stories like this and some of the suggestions leave me open-mouthed.
First let me apologize in advance because I am not bashing.
I have been training horses for 49 of my 61 years and have never had a horse react as has just been explained, nor have I ever had to use some sort of device to accomplish what I need done.
We never used nose chains either -- not even on my grandpap's stallion during breeding because we "handled, handled, handled", our horses from front-to-back and top-to-bottom every day. We had and still have their respect because they want to give it.
Accept for my Arab, I have never owned a horse that, at any age, I couldn't walk up to them in the field, put my arm around their neck and give them a tube of wormer.
The Arab was the worst horse I have ever owned to worm when I rescued him 15+ years ago. I did have to halter him because he wouldn't open his mouth and was making a monkey face that even his mother wouldn't love - lol lol
I know where those teeth end in his mouth, so I would quickly put that syringe in the back of his mouth and push the wormer in.
Then I would have to walk him and rub his "adams apple" at the same time until he swallowed. If I didn't, he would hold the wormer in his mouth until I walked away and he'd spit it out.
This is where "handling that horse every day before it gets to handling you" is important. I think the modern catch-word for that is "imprinting".
Young horses especially need their eyes, noses, mouths, ears, private areas, anal areas handled often, so when they really need to have something done in one of those areas , they won't do what your two-year old did with the wormer. He has just learned a very bad habit that is now going to be hard to break.
Again, I really do apologize if I sound harsh, because I don't mean to be -- that is the problem with keyboards --- no voice inflection.
This young-un' needs a lot of hands-on every day. If he doesn't get it, he is going to end up sour and misunderstood and his dollar value will go right down the drain.
He's at the age, where he should stand quietly in the pasture to have his hooves at least picked up and rubbed on, stand quietly for brushing with nothing more than a binder twine around his neck, and again, let someone put their arm around his neck and put the wormer in his mouth --- even following that with a "GOOD BOY!", scratch on the neck, and a horse treat