Any kind of restraint can be made to hurt.
A properly applied twitch should not hurt very much at all. As saddlesore mentioned, it should get the critter to release endorphines - naturally produced narcotic substances.
Because of the leverage that can be applied, it should not be used by someone without education, experience, and supervision. it's very easy to injure a horse and cause and/or exacerbate bad behavior.
For dental work, I'm a fan of an equine dentist. A horse should be doped up and have dental work performed by a professional. We're lucky to have a very good equine dentist here in AK.
*Some* vets are able to do dental work, but two things vets don't get enough of in vet school to be come proficient at and are expected to be experts on are teeth and feet. there are specialists for each.
