There are about half as many horses in Iceland as there are people, about 175.000, and they are horses, not ponies, although they are shorter than most other breeds, but they're strong and bulky. This characteristic, along with the fact that they put on a fluffy winter coat, helps them survive the Icelandic winter as they are kept outside year round, even in the biggest of blizzards. They originate from Scandinavia and were brought to Iceland by the first settlers, the vikings, in the early 9th century, and have been isolated since then. One of the oldest laws in Iceland, dating to 982, says other types of horses are not allowed into Iceland, and now horses that leave Iceland are never allowed to return. It's like a reverse North Korea for horses, you can leave but you can't come back. This is done to protect the Icelandic horses from diseases they might not have immunity from, as they've been isolated here for more than a thousand years.
The Icelandic horses are also quite special because they have five different gaits, or five different ways of running, whereas most horses just have three (out of the four common ones - walk, trot and canter or gallop). The fifth gait, the purely Icelandic one, is called tölt and is very smooth. In fact it is so smooth I've seen a rider on a running horse drink champagne from a glass. It's like the body of the horse, and the rider, just glide through the air. I've never been given an explanation on why the Icelandic horses can do this, but I have my own theory. I know for a fact that the Icelandic horses can pass through any terrain in Iceland, including rocky beaches and lava fields, where other horses would simply brake their legs. For this they have to be light footed but sturdy, lifting their feet as they walk or run, as they do when doing the tölt.
In the 1800's the US army did an experiment where they rode all types of known horses from coast to coast in the US, to find the perfect all-terrain horse breed. Only two breeds completed the journey, the Mongolian and the Icelandic breed. The US army planned on buying a shitload of these horses, but then the railway came along and there was no longer a need for them.