When I was making the life list I put "See a reindeer in Iceland" on there sort of offhandedly, because it seems like reindeer are a thing that happen in the northplaces and I vaguely remembered reading once about someone taking a reindeer sleigh ride. So it seemed like reindeer should be everywhere. It didn't really occur to me at the time that Iceland, being an island and all, probably wouldn't have much in the way of native animal life and that large mammals would probably have been brought there by someone.
It took three tries for the reindeer in Iceland to stick, with a herd finally making it through the winter in the mid-1800's, and not a single person while I was there seemed to care about them at all. Perhaps that's the difference between East Iceland and West Iceland, but the reindeer weren't even among the list of animals one of our tour guides recited.
It turns out that what they really love in Iceland is their horses. Their horses are built from the stock of the ones who can deal with the climate and the volcano eruptions, but they're also strangely delicate--so many years of isolation has made it so that they can withstand the inside of the earth coming out but not any sort of foreign virus. As a result, Icelandic horses aren't allowed back in the country if they leave it. Reindeer might be a symbol of the frozen north, but these compact little horses with adventure and hard luck in their past and future simultaneously, just pressed right into their bones, are so very Icelandic. And with their manes blowing in the unrelenting wind among the steaming hillsides, much more picturesque than an average reindeer.