Iceland does not have any native deer, antelope, moose or anything of the like. Reindeer were introduced from Norway for farming in the late 18th century. Reindeer husbandry never worked out in Iceland and the animals were never domesticated. Today only a small amount remain and live in the wild in East Iceland. I would have completely missed our two sightings if it weren't for Dave's eagle eye.
At this time of year, the pregnant females are higher up, giving birth. Those that were visible were either bucks, juveniles or non pregnant females. This guy had a great set of antlers.