Horses first came to Iceland in the late 800's with the Vikings. They like their particular breed of horse's so much that you cannot bring any other breed of horse to Iceland. If a horse leaves Iceland, it cannot come back. So if someone is competing in something, they don't take their best horse with them, since they will have to leave it behind somewhere. They are small, just at the bottom of the cut off for what is considered a horse versus a pony. They have super cute bangs that hang down into their faces. They are well adapted to their environment.
We were amazed at how many we saw. They were everywhere in lots and lots of fields. We were wondering why there was so many. Then I saw horse on the menu in a couple of restaurants and the pieces fell into place a little. They aren't just for riding, they are also for eating. I couldn't eat it.
There are also several horse farms where people ride them, train them and rent them out to be ridden.