The Icelandic horse is a breed of horse that has lived in Iceland since the mid-800s, having been brought to the island by Viking settlers.
There are roughly 100,000 Icelandic horses in Iceland, and relatively few abroad, owing in large part to centuries-old Icelandic legislation that prevents any Icelandic horse from returning to the island once it has been taken to another land. Icelandic horses are bred in closed pedigrees because they must be traceable back to Icelandic ancestors.
Icelandic horses have been bred only with horses from Iceland since the Middle Ages. Icelandic words are used as names for Icelandic horses, words which describe their color etc Sometimes names from Norse mythology and Icelandic nature are used.
Some examples include Grána which means "grey mare"; Teitur, which means "the happy one" or Hrímfaxi which means "the one with frost in his mane". Wikipedia, the free encyclopedia, photograph below from Malene Thyssen.