I agree with everything that has been said so far.
Also, riding is frequently used as a form of therapy for mentally or physically disabled people because it provides people with a sense of self accomplishment, and goals, and a way for people to focus their minds. It's been proven to improve physical and mental health, from the teamwork and connection, and being around animals (which also has a therapeutic affect.
I totally agree with Tessy, horse riding provides patience, self control, many qualities that are useful in the everyday life. There's a quote that I love: "horse riding is the only individual sport which is practiced at 2" it means to me that you have to create a strong relationship with your horse. It mixes body activity (sport), mind (concentration, reflexion) and heart (a rider without heart can't be a real rider) and all of this is a huge benefit from that sport :)
Horse riding is first a sport so it brings sport benefits. But there's also relationships with the horses. That's to me the most important part. It permits to develop altruistic qualities because this sport isn't only on your performance but also on the horse's performance. I know I'm more patient and attentive thanks to horse riding :)