Thoroughbred horses

According to Wikipedia, The Thoroughbred is a horse breed best known for its use in horse racing. Although the word thoroughbred is sometimes used to refer to any breed of purebred horse, it technically refers only to the Thoroughbred breed. Thoroughbreds are considered "hot-blooded" horses, known for their agility, speed and spirit.

The Thoroughbred as it is known today was developed in 17th and 18th-century England, when native mares were crossbred with imported Oriental stallions of Arabian, Barb, and Turkoman breeding. All modern Thoroughbreds can trace their pedigrees to three stallions originally imported into England in the 17th century and 18th century, and to a larger number of foundation mares of mostly English breeding. During the 18th and 19th centuries, the Thoroughbred breed spread throughout the world; they were imported into North America starting in 1730 and into Australia, Europe, Japan and South America during the 19th century. Millions of Thoroughbreds exist today, and more than 118,000 foals are registered each year worldwide.

Thoroughbreds are used mainly for racing, but are also bred for other riding disciplines such as show jumping, combined training, dressage, polo, and fox hunting. They are also commonly crossbred to create new breeds or to improve existing ones, and have been influential in the creation of the Quarter Horse, Standardbred, Anglo-Arabian, and various warmblood breeds.

Thoroughbred racehorses perform with maximum exertion, which has resulted in high accident rates and health problems such as bleeding from the lungs, low fertility, abnormally small hearts and a small hoof to body mass ratio. There are several theories for the reasons behind the prevalence of accidents and health problems in the Thoroughbred breed, and research continues.

Miniature Horses & Ponies

From the web site USA Miniature Horses Association i found some history of the miniature horse. The History of Miniature Horses & Ponies

The earliest history of miniature horses was in the 1650 A.D. records at the Palace at Versailles where King Louis XIV (The Sun King) kept a vast Zoo, replete with unusual animals, including tiny horses. 

In the mid 20th Century, many distinct small horse breeds emerged including the Miniature Shetland Pony, the Miniature Toy Horse and the Midget Pony.  These breeds formed this historical foundation for the Miniature Horse breed.

Arabian Horses

From the web sit of the the American Arabian Association I found a little history about this great breed. (From the ancient deserts of the Middle East evolved the oldest known breed of riding horse, the Arabian. Now one of the most popular breeds in America, the Arabians' incredible energy, intelligence and gentle disposition allow riders to excel in most equine sports and activities. Today, Arabian horses spend as much time on the trail as they do at horse shows and other competitive events.
For thousands of years, Arabians lived among the desert tribes of the Arabian peninsula, bred by the Bedouins as war mounts for long treks and quick forays into enemy camps. In these harsh desert conditions evolved the Arabian with its large lung capacity and incredible endurance.
Historical figures like Genghis Khan, Napoleon, Alexander The Great and George Washington rode Arabians. Even today, one finds descendants from the earliest Arabian horses of antiquity. Then, a man's wealth was measured in his holdings of these fine animals. Given that the Arabian was the original source of quality and speed, and remains foremost in the fields of endurance and soundness, he still either directly or indirectly contributed to the formation of virtually all the modern breeds of horses.)

The American Quarter Horse

When you look up the Definition of a Quarter horse this is what I found, Wikipedia defindes it as (The American Quarter Horse is an American breed of horse that excels at sprinting short distances. Its name came from its ability to outdistance other breeds of horses in races of a quarter mile or less; some individuals have been clocked at speeds up to 55 mph (88.5 km/h). The American Quarter Horse is the most popular breed in the United States today, and the American Quarter Horse Association is the largest breed registry in the world, with more than 5 million American Quarter Horses registered.

The American Quarter Horse is well known both as a race horse and for its performance in rodeos, horse shows and as a working ranch horse. The compact body of the American Quarter Horse is well-suited to the intricate and speedy maneuvers required in reining, cutting, working cow horse, barrel racing, calf roping, and other western riding events, especially those involving live cattle. The American Quarter Horse is also shown in English disciplines,driving, and many other equestrian activities.)

As a horse owner myself I would have to say that this is my favorite breed of horse. They are great horses; there personalty's, body build, and variety of  colors makes this one of the best all around horse.