LKL and kfisherx, you said it best. It is the joy of communicating with a hon-human and non-demanding species in a form of intimacy that you can't with humans. I think it might have a lot to do with Asperger's.
As a child I grew up around horses and they were just part of life. I had a bad riding experience as a teen, that put me off them for a time. Now, at 50, I'm taking up riding again this year.
I find the best relationships in my life are with animals. I have four large dogs I live with, and a cat, and have no desire for a human in the house with us. Too complicated. My dogs are my friends, honestly. They appreciate solitude and silence, they keep me calm, they go for walks in the woods with all the joy that I myself find there. They are interested in my safety and well-being, more than most humans ever were. At this point in my life and my journey toward self-awareness, I want to explore a relationship with a horse again.
Carole, I'm wondering if you have read some books by Temple Grandin? And if you are aware of http://www.howrse.com (careful, it's addictive).