The instrument being used is called a Speculum. Without the Speculum it is not possible for the dentist to do a really good job on the furthest back teeth, or to fully visualize the whole mouth.
I have a dentist that does not need to twitch most horses to do their mouths; if he does need to restrain a horse, he generally prefers a very light dose of sedative because the OWNERS seem to prefer it, but he has no problem with a twitch.
He's brilliant, has a brilliant understanding of horse behavior and responses. He puts on the speculum, they champ at it a bit('you mean I have to not eat anything for fifteen minutes? Sacrilege!!!'), he gives them a little time to realize it's inconvenient rather than painful, and he does half the work, removes the Speculum, gives them a rest, we chat, and then he does the other half of the work.
I've also seen him use a speculum only for the back teeth, and do the rest of the mouth without it.
Twitching is not painful to a horse, and it doesn't traumatize or damage them - IF used properly.
Many times the problem is NOT the twitch, but the inept and unskilled APPROACH to the horse to put it on - too - a horse that's been hit in the head with a stick is going to see the twitch as 'oh, no, not another stick, I'm not going to stand still for this - GOOOOOD BYE!'
It is very important to approach the horse properly, and not try to 'muscle' the horse or 'over restrain' it to get the twitch on. MANY people approach the horse with the twitch, in a very unskilled fashion.
If it is done correctly, it works very well for restraining a horse in emergencies or for specific procedures.
It can be the difference between life and death for a horse, and every conscientious horse person should have a twitch and understand when and how to use it.
Otherwise they are taking a terrible chance that something will happen some day and they will be completely powerless to cope with it. It only takes one thrashing, struggling horse dying while you look on able to do nothing, to convince you.
Horses have been twitched to prevent them from struggling in a wrecked trailer with the emergency vet still an hour away, or while a sedative takes effect, or to prevent them from struggling when they are tangled in wire. They've been twitched when they get trapped in a ditch or obstacle.
And yes, it's quite routine to twitch a horse for medical procedures.
If the owner refuses to allow a tranquilizer, if the horse's reaction to a tranquilizer is unknown or if he's allergic to several tranquiliers, if you cannot weigh the horse or get any information about possible allergies to medications, a twitch can be a far more prudent choice.
When time (and information!!!!) allows, a medication like Ace or Rompun can be used - but many times, a medication cannot be used at all. It's an emergency, the animal is in shock, or any tranquilizer would depress the Central Nervous System even more (than the injury or what have you).
SOMETIMES - a sedative is useless. If the horse's circulatory system is depressed, a sedative won't circulate properly or take effect.
How does the twitch work? Not by pain. But by a simple fact that has been understood by horse people for many centuries: A horse can only think of one thing at a time.
The pressure on the lip isn't painful, but it does take their attention off of other things.
Many horses resist being twitched because either they realize that it means they will have to hold still for a while, or because the twitch has been put on too tight (becomes less effective and more annoying) or too loose (horse's full attention is on what ever else is being done to him, and it's something he doesn't like). Or again, as I mentioned, the person approaches with the twitch like Atilla the Hun.
OR....because the OWNER dislikes the twitch! Yup! Some owners are just awful about their baby being twitched. We used to have a vet years ago who would walk up and start telling the horse owner horrible, horrible jokes and holding their rapt attention by keeping up a constant fast paced chatter. It was hysterically funny to see the horses accept the twitch quietly, and get through their stitches or wound cleanup peacefully, while the vet kept up his constant stream of jokes and stories.
As long as the owner was distracted, the horse would accept the twitch, stand quietly restrained during his procedure, and end it without any objection. Quite often the vet would put on the twitch, hand the handle to the owner, and go about his business, say, picking dirt out of a cut and stitching it up.
The vet then would rub the horse's nose and face gently, praise it with a soft voice, and move onto his next 'Perfect Patient'!!!!! LOL!!!!
Once I asked him about it, and he ribbed me and said I was perfectly welcome to watch some time what happens if he works while he has Laryngitis!
On a horse the upper lip is a hard, firm tissue unlike a human lip, it is not so very sensitive like a person's upper lip. If you were to bend one finger sharply, keep it bent, and then squeeze on the fat part of the finger right at a joint, using the thumb and forefinger of your other hand, that's what being twitched feels like. It's an odd sensation, not painful, nor pleasant, just rather odd and it holds their attention.