This article explains the difference between the training practices of desensitisation (controlled exposure to novel objects: horse habituates to the stimulus and stays under observable reactivity threshold) and flooding (intentionally, and unacceptably in my view, taking the horse over threshold by forced proximity/exposure to something that frightens them, until a fear response is no longer seen).
Important to note that once a conditioned fear response has been established (the horse always moves to the far corner of the stable, away from us, when we approach with a saddle, for example), the recommended systematic desensitisation and counter conditioning treatment programme has to be a staged approach across many training sessions, not simply within a session.
So whilst we use the term positive reinforcement to describe the “good thing” that we add to the environment (e.g. treat/scratch), sometimes together with a clicker/marker, the “active ingredient”, so to speak, is classical/respondent conditioning rather than the so-called quadrants of operant conditioning.
If you saw The Secret Lives of Dogs (UK, Channel 4) episode on fear-aggressive dogs, it showed good examples of systematic treatment programmes, using gradually decreasing distance (over weeks or months) from the fear-inducing object. This changes the fear emotion to an association with something good, resulting in calm, relaxed behaviour where previously we had seen reactivity. The benefit of this approach is that, done correctly, it has a reliable, long term effect, with obvious practical and emotional advantages for the human half of the partnership too!