Dear Tuckerup,

I have been a horsewoman my entire life.

That isn't a stupid question at all.

First let's talk about horses in general. In nature, they are a prey species, and their two primary defences are (1) running away or (2) bunching up with the herd.  So these two reactions are inborn. But they've been domesticated for a long time -- it's many centuries since predators are a fact of life.  And since they've been domesticated, various traits have been selected for (or deselected).  So these reactions in a domesticated horse aren't as strong as in a feral horse.

Now let's talk about your average, run-of-the-mill horse.  They (like people, dogs, cats etc.) have very different personalities. Some are timid or fearful; some are entirely self-assured; some have different phobias, some are so dullard nothing moves them, and so on. 

In encountering a person who is afraid of them, a timid horse (for example) might herself react with fear.  A more self-assured or bossy horse might look around for what is making the person afraid.

Now we'll talk about horses used in therapeutic riding programs (hippotherapy).  Most hippotherapy programs serve people with all kinds of issues, including mobility (wheelchair users)  movement disorders (spasticity or unpredictable movements) to vision issues to ... well, lots.  First, potential therapy horses are evaluated for temperament.  A good therapy horse has a kind, forgiving, and non-reactive temperament.  Then, before the horses become therapy horses, they have lots and lots of training, which ensures that the horses react with calmness to unusual human behaviors.

Then, the hippotherapy program probably starts where the client is.  If the client is fearful of even getting close to a horse, maybe the first therapy horse is quite small, and all the client does is learn how to interact with the horse without fear or anxiety.  The first sessions might be standing (or sitting) next to the horse, and perhaps  (for example) touching the horse with one finger.  Then perhaps moving to touching the horse more completely.  Most horses love being brushed and petted.  So maybe that's the goal for the first set of sessions: having the client be at ease and maybe even enjoying brushing the horse.

Eventually, if riding the horse is in the picture: again, it's a stepwise process.  Again, since most hippotherapy programs serve clients with all kinds of disability, the riding part can start quite slowly: maybe just sitting on the horse while "sidewalkers" (people who help the client by holding on to him or her) are there, and the horse's head is held by the leader.  The client is never responsible for stopping or starting or steering the horse until she is ready to do so. Some clients never get to the point of having that responsibility, and that is fine too.

About 10 years ago, I had the use of a covered riding area that was also used by a hippotherapy program.  One of the clients (an adult) took about 20 sessions to get comfortable sitting on the horse and walking more than 5 steps at a time.  The therapists never pushed the client to do more than she could handle. 

That's probably more of an answer than you wanted or expected, but maybe it will be helpful for other people who are considering hippotherapy for themselves or for another.