Yes, there are reindeer in Iceland. In fact, the Icelandic reindeer population is believed to be descended from the original herd that was brought to Iceland by the first settlers over 1,000 years ago. The Icelandic reindeer are quite different from the larger, hardier reindeer that live in northern Europe and Asia, and they are well adapted to the rugged terrain and harsh climate of Iceland. They are a beloved part of Icelandic culture and history, and they have become an iconic symbol of the country.