Wildlife in Iceland is not very diverse. Biggest and only wild hooved mammal is Reindeer.
Reindeer were introduced from Norway late in the 18th century originally for farming, but reindeer husbandry the Scandinavian style did not tempt the Icelanders, and the animals were never domesticated. Today the wild reindeer live only in South East and East Iceland, mostly at higher elevations in summer but seek lower grassland, closer to the coast in winter. While their primary habitat is in the deserted expanses by Snæfell, reindeer are seen every year in the territory extending from Vopnafjördur in the north to the Glacier Lagoon in the south.
Here are pictures of some Reindeers that I met in Hornafjordur (south east corner of Iceland) in past 4 years.