All therapeutic riding teachers come in to teaching either stronger on the riding side or stronger on the disabilities side. If you are new to working with childen with Autism Spectrum Disorder (ASD), it is important to understand that their behavior is always trying to communicate something. The better you know the child, the easier it is to figure out what they are communicating. This article from the Indiana Resource Center for Autism gives a good description of such behavioral communication and some good examples:
I highly recommend exploring their website for more great information about ASD!
Note: This is not professional advice, this is a blog. I am not liable for what you do with or how you use this information. The activities explained in this blog may not be fit for every rider, riding instructor, or riding center depending on their current condition and resources. Use your best personal judgement!