Yes, Phil, horses have the same kinds of effects on people as dogs have.

My wife works with equine-assisted psychotherapy, which uses horses to help kids and teens who have mental, behavioral, emotional and social problems, and/or who have been abused in various ways, break through some of those problems and become better adapted at dealing with themselves and others. Often a kid (or adult, for that matter) cannot or will not talk to a therapist, but they "come alive" when dealing with a horse, and sometimes will even tell the horse what's bothering them. They find that working with a horse is comforting, and the horse will "listen" to whatever they tell it.
There is a residential treatment center for mentally- and physically-handicapped people near where we live, and it has a horse therapy program, as well. Some of their residents who can't walk find that they can ride a horse, and a couple of the residents, for the first time in their lives, have been able to walk after several sessions of horseback riding. It stimulates the muscles in the legs somehow. It's pretty interesting work, and amazing to see the big smiles on their faces as they gain confidence from rding and grooming the horses.