My horse has been dropping a lot of feed when he eats. I've also wondered if he had a sore tooth, but it turns out he just had very pointy and sharp teeth that needed to be filed down, or "floated".
He was sedated, then they set to work, filing his teeth down, squirting water into his mouth, filing a bit more, checking each time to see if it was enough or if he needed a little more work.
Finally they were done. We left the horse in the corral, where the others wouldn't bother him, until he was completely awake. Then I let him out to rejoin the others and eat his evening hay.
I'm sure glad that modern human dentistry is far ahead of equine dentistry.