From the first horse like creature to have evolved with one toe instead of three, all modern equids were born. These Include Donkeys, and Zebras and three possible ancestors to our riding breeds. There were countless varieties of equids in prehistoric times but only these remain today. It is debatable that even though there were numerous forms of the horse between Eohippus and Equus Caballus, the modern horse most likely derived from 3 and increasingly more proven 2 original types.
The "Forest Horse" inhabited the wet wooded lands of northern Europe. It was a hairy, non-migrating horse and was able to withstand winters because of its stocky body type.This is the primary ancestor to our "Cold" breeds which have had minimal or no influence fro the other two types.
The "Przewalskii" or Asiatic Wild Horse (pictured at the top of the group description) remains in it's original form.. It has had minimal or no influence in modern breeds. Perhaps through domesticated descendants having been shipped to Europe, thousands of years back. If this link exists to the "Przewalskii" this could likely be the real difference between the old Warmblood breeds and "Crossbreds".
The "Tarpan" was the most succesful of the primitive horses to be domesticated. It's descendants were traded wordwide & as a result most horses available today of non Draft breeding are either direct descendants of the Tarpan (Hotbloods) or some composite of hot & cold.
Which fourth type do you propose? And how does it fit with other hypothesis like mine.