I'll probably be more stressed that my horse.
I know the feeling!
But I also have had a couple of weeks of reminders about how much my stress affects their stress... Relax, worried mama!
It truly isn't that big a deal to get their teeth rasped. It doesn't hurt, and a good vet does it really quickly.
Sometimes Stardust lets John, my vet, do it without any fuss; sometimes he's not in the mood and John gives him just a light sedative to calm him down a little. And he holds no grudges afterwards!
So while I think your idea of working in their mouths is a great one, don't put off calling the vet while you get them ready -- in all likelihood, they're not every going to like this very much, and for me, it falls under the "necessary, but over quickly" category -- like paste wormers, etc.
And it can make a HUGE difference for them!
They can get weird physical stuff, aches, gait strangeness, all sorts of stuff going wrong when they've got a spur or something going on with their teeth.
I have had mucho dental phobia over the course of my life, too, and am paying for it with multiple dental trips and procedures (even as we speak I'm doing a chipmunk impression w/a wisdom tooth pulled on Thursday...have bone graft surgery (for the 3rd time) coming up in the next couple of months, etc.)...
The good part about all of this is that it's demystified the process for me and a lot of my phobia has gone away -- I guess this is bound to happen when you're in the dentist's office almost every week for almost two years. If you have a vet you like/trust, Annie, ask him/her to explain exactly what they're looking for, what they're doing to address it, etc. -- this may help a lot to cut down on your fear factor.
But if you're seeing bits of half chewed feed it's very likely that someone has some teeth wackiness going on that needs to get fixed -- 10 minutes, tops, and it will be done!
"Ours is the portal of hope. Come as you are." -- Rumi www.imaginalinstitute.com