This pretty much sums it up on the origin of the word "medicine Hat" hope it is useful to your purpose
Written by Rena Sherwood
A "Medicine Hat" horse is not a horse of a particular breed, but of a particular color. This is an unusual pinto pattern where the base of the horse is white, but the ears and around the entire top of the head is brown, black or roan. The horse looks like he has a tight cap on. Legend has it that Native American tribes, especially Plains tribes, called the spot a "Medicine Hat" or "war bonnet".
The important distinguishing characteristic of a Medicine Hat is the head. The rest of the body can be of any other pattern. But in order to get a white head and colored ears and cap, most Medicine Hats or Wart Bonnets are mostly white in color with very few other colored patches. They very often have pink muzzles.
What's The Big Deal?
The Medicine Hat marking denoted a horse of superior ability in some way. Some tribes had legends where a rider of a Medicine Hat horse would never be hurt on the back on the horse. Some were said to be able to warn his or her master of danger, or to be able to find game in the most barren of landscapes.
A blue eyed Medicine Hat was especially prized for his or her unusual beauty. The blue eyes of the horse (known often as "sky eyes") made the horse seem otherworldly or ghostly. However, many white faced horses tend to have blue or odd-colored eyes. Because of their mostly white hides, magic or power symbols were often added to him.
Medicine Hats were also considered incredibly lucky. In wearing a magic symbol, the horse personified the magical qualities of a tribe. If your tribe lost its Medicine Hat, misfortune was soon to come, because all of the good magic was gone. Please keep in mind that his is a very simplified explanation for a very complex belief system.
Medicine Hats Today
Modern culture probably wouldn't know much about Medicine Hats if it wasn't for a book entitled "San Domingo: The Medicine Hat Stallion" by famous children's author Marguerite Henry (who also wrote "Misty of Chincoteague"). That book probably would have faded into obscurity if it were not for the fame of the author and a popular Breyer model horse made of the main character, San Domingo.
The Medicine Hat coat variation still exists today and is considered just as valuable now as in the Old West. They can be found in several breeds, including the Paint Horse, Spanish Barb, Mustang, Appaloosa and crossbreeds (called a "grade" horse). Sometimes the coat pattern pops up in ponies as well as horses.