Equus caballus is split into three broad types. These types represent different wild populations that were absorbed.
1. The steppe horse. This was the first horse to be domesticated and originated on the Asian steppes. The steppe horse refined into the modern Turkemen and Akhal-teke horses, the Arabians and Barbs of north America, and reaches its ultimate form in the Thoroughbred. The descendants of the steppe horse are refined, light, and very fast. They have fine coats and tend towards sparse manes and tails. They are often called "hotbloods." (Contrary to popular belief, the three founding sires of the Thoroughbred were not all Arabians - at least one was a Turkoman. The purest remnants of the original steppe horse are the Tarpan and the Caspian, although Icelandic horses closely resemble the Tarpan and may also be close to pure "steppe."
A modern American Thoroughbred is "walked out" after a race (it was blistering hot that day).
2. The forest horse. Originating in central Europe, the forest horse is a stocky, heavy horse with much more "hair" on it than the steppe horse. Forest horses have feather over their hooves. The forest horse has been bred up in size. And up. And up. The modern descendants of the forest horse are the various draft breeds, which include the biggest breed of horse in the world - the Shire. Draft horses are also sometimes called coldbloods.
A roan Belgian carries her own harness...she's about to be loaded onto a trailer. This is a fairly small draft horse.
3. The hill horse. Originated in northern Europe. Small, smart, and scrappy, hill horses are tough, survive on minimum forage, but don't breed up in size well at all. Like the forest horse, they tend to have a lot of hair. Actually, they often have even more hair. The modern descendants of the hill horse are all the various pony breeds - tough, often difficult to handle, but easy and cheap to keep.
A Shetland pony in a standing stall. His mane has been trimmed because it gets so hot here - it should be all the way down to the bottom of his neck.
All of our modern breeds of horse, every one, are descended either from one of these three types or from specific interminglings of the two.
Most light horses are "warmbloods" - created by mixing coldblood lines with hotblood ones. This includes the modern American stock horse - the most popular breed of horse in North America is the Quarter Horse - as well as sport horses and the highly refined, carefully bred Warmblood breeds of Europe. (Note that warmblood, small w, can be any light horse, but Warmblood, large w, should only be used to refer to a horse registered with a Warmblood registry).
A Dutch Warmblood stallion doing high level dressage. Source: Fotoimage via Wikimedia Commons.
Draft ponies such as the Haflinger, the British colored cob and its Irish equivalent (often called "gypsy" or "tinker" horses), and the Norwegian Fjord are a mix of coldblood and pony blood.
A classic "draft pony" - the Norwegian Fjord.
Sports ponies are often made by crossing ponies and hotbloods - pony/Thoroughbred crosses are popular in Britain. Some riding pony breeds, such as the modern Welsh Pony, have a fair bit of Thoroughbred in them.
Me riding a pinto sports pony, probably a Paint/Welsh cross. (Yes, I am that short. That is really a pony.