Iceland has its own unique horse breed that came to Iceland with the first settlers. Archaeological digs have revealed that the ancient breed is a descendant of a now extinct breed except for in Iceland, where the isolation has kept it preserved.
In addition to the walk, trot, and gallop as found in typical horse breeds, the Icelandic horse has two extra gaits which come naturally to the horse (they have not trained to perform the gaits), the tölt and the skeið. The tölt is described as a four-beat ambling gait, famous for being so smooth that you can drink champagne while riding as the rider remains quite still. The other gait is called the skeið and is used in pacing races sometimes reaching up to 50 km/h. A chance to ride this horse is definitely a reason to visit Iceland.
There are many different horse farms and companies offering a variety of horse riding tours. Íshestar, for example, offers multi-day riding tours as well as one- and two-hour riding tours in natural parks close to Reykjavik for riders of all levels of experience.
Another company, Eldhestar, offers a wide variety of tours as well. There is an option to combine half-day, full-day, or multi-day tours with a variety of other activities such as Northern Lights tours, spa visits, wilderness treks, volcano tours, or food tours. The farm keeps about 350 horses during the summer and about 100 during the winter, so there is the option of going year round.
In the north of Iceland, close to Akureyri, Polar Hestur has been offering horse riding tours for more than 30 years. They also offer multi-day, full-day, and half-day riding tours that take you deep into natural areas of North Iceland, on mountain paths and along fjörd paths. Some of the tours can be combined with visits to incredible places in the area such as Lake Myvatn and Goðafoss Waterfalls and Ásbyrgi Canyon. All of these places are gorgeous all year round.