Does the food reward create a “mouthy,” nippy horse?
Sometimes it can. If that seems to be happening, you can switch to giving the reward from a special container used only for that purpose. Most horses will distinguish the source, and will not nudge for treats unless the container is present. That way you can put up with the eagerness for treats during the re-training, then eliminate the treat container and the associated mouthiness once you have achieved compliance. You also can teach the horse to wait for the offer.