It seems that the oldest Rangifer Tarandus fossils are from Siberia from 2.1 million years ago, while the oldest in North America/Greenland are from about 1.6 million years ago. That was during the height of the last Ice Age. So, the best guess is that they migrated across The Bering Land Bridge, rather than across sea ice from Norway to The Shetland and Faroe Islands, and on to Iceland, and then to Greenland. It seems more likely that those that got to Iceland came from Europe,(but not certain). But that those in Greenland mark the end of the migration from Siberia. Those in Greenland belong to The North American subspecies, while those in nearby Iceland belong to The Eurasian subspecies. They are all in the same species, and can mate and have fruitful offspring.
https:en.wikipedia.org/wiki/Boreal_woodland_caribou
I will read the stories in this book and see if "The Great Reindeer Trek" is a special single event about which I was aware in real time, or if it just refers to the very long distance they migrate each year for the change of seasons and birthing their young.
Link to the book:
True Aviation Comics Digest 2