By equipment I assume you mean tack. The halter is used to lead, lounge or tie your horse. The bridle is a headstall, bit and reins and this helps the rider direct the horse where he wants the horse...
Farm work, battle, pulling carriages, transportation, pleasure riding, mail services, sports, and many more. They still are used for many of those things.
Many things, if a canal boat broke down they would tie a horse to the boat and the horse would walk down the track outside of the boat - for transport - to carry famous people - at weddings if you...