Miraval resorts are known for their equine experiences. I’m not a horse rider at all, but felt I had to learn more about what Miraval offers.
And yes, they do offer both riding and non-riding equine experiences, and they are all open to non-riders, beginners, or experienced riders. 
The experience I chose to do was the Miraval Equine Experience. As the description outlines, this experiences allows you to “work alongside our specially selected horses and expert facilitators to practice living life in the moment. Horses are creatures of the present, unconcerned with past regrets or future drama. They offer a way to help us notice personal patterns that could be restrictive in this exercise and life.” 
I signed up for this fee-based session, and was surprised that I was the only guest – so I had a personal session with the equine expert, Leigh, who spent some time chatting with me, and besides learning about my horse experience (none, other than watching my daughter, and maybe riding a pony years ago), she also asked me about my work/ life choices, and how I operate my days, how I respond to stress, etc. etc., Then she led me to a field with 10 horses to meet them, and then ultimately pick the horse I would be working with. Little did either of us expect that Pepper would walk up to me right away, and sniff me out. I took some time to say hello to the other horses, but ended up working with Pepper, of course.
A horse with one blue eye was really special – but it was the brushing of Pepper’s coat, and grooming her, and then leading her around the field that was both meditative and instructional. Horses don’t tell you they don’t want to do something, and they only follow if they trust you, and you show no hestancy. A very fun a morning in Austin, Texas, as I embraced my inner cowgirl.
Have a look at Miraval Austin’s equine experiences – and let me know if you’d like to go. https://www.miravalresorts.com/austin/experiences/equine
As a Virtuoso travel advisor, I’m pleased I can extend some extra perks when you book your Miraval adventure through me.