Equipment is "basic":
A horse and tack
bow and arrows
a field to shoot in
lessons!There are many
|An Eastern Horse Bow|
|A Basic Horse Bow|
|Some of the bows from the Flying Duchess|
Traditionally a horse bow is a style of recurve bow due to the fact that it is shorter and will not interfere with your riding or hit your horse!
You can find additional information on mounted archery and horse bows here and here and here!
Hopefully I have inspired you to do something new!!