I am in the middle of getting an Asperger's diagnosis. My psychologist is very sure I have it.
One of my interests was horses when I was a child. I knew EVERYTHING about them. My mother went ahead and put me in riding lessons.
It helped my balance tremendously, and it gave me an emotional outlet. Somehow, I connected to horses, understood them, and was happy when around them like nothing else.
I started around 10. We ended up getting me a horse, and I trained her from a baby. I learned more empathy and had more fulfillment because of that than anything else. Today, that horse and I are the best of friends. I even took her to college with me.
My horse is my stability when people are bewildering. I always feel accepted and understood by my horse. I am SO glad my mother got me into it. You don't have to own a horse, though, to bond with it and benefit from it.
I highly recommend it. Just make sure the trainer knows why and is willing to work with you. I know that it can't hurt to try.
If you want to ask me more, just send me a message. I've been doing stuff with lessons and horses for 12 years now.