The only land mammal native to Iceland is the Arctic fox (Alopex lagopus). The occasional polar bear is driven off course and shows up in Iceland but there has never been a native population there. The foxes are believed to have drifted there by accident, on icebergs from Greenland. During winter the foxes follow male polar bears on the ice banks (females and cubs hibernate but adult males don't), hoping to eat the leftovers of the animals the bear hunts, and when the thaw comes some foxes get trapped in icebergs floating south in the ocean.

Arctic foxes show up in Viking settlements and their winter pelts are very pretty but I don't know if or how often they were hunted.

On the other hand Iceland is very rich in seals and nesting sea birds. It was the last place on Earth where the great auk (Pinguinnus impennis) survived before it was hunted to extinction in the 1850s.