I find grooming horses (and cats) to be very calming for myself. There is some technique so if you can ask the riding center folks to show you on a gentle horse, and just do that regularly for a while, you might start to have a sense of reciprocal communication with the horse. Some websites describe horse body language, I love trying to figure that out.
Also it's good exercise! Many horses like being groomed, esp. certain areas, and this time of year they need to get rid of winter shedding.
They are large and warm, and on a nice day it's just so soothing. Bonding with a horse this way can be really wonderful, takes time.
Also I like to spoil them with treats! That can give insight into their positive emotional expressions! :-)