In fact, Greenland was always mostly covered in ice, though it had some very nice and inhabitable areas to spare along the giant island's coast -- somewhat like Alaska, though Greenland is even bigger overall. Its original Norse settlement founder, Erik the Red, is famously said to have given it the name "Greenland" for marketing purposes in order to attract settlers. They did in turn set up thriving settlements in the inhabitable slivers of land there that were indeed green. And ultimately, those settlements died out centuries later, for reasons that are still not totally understood.
Possible causes include a period of intensified cooling, plague, and raids from foreign areas, all of which would have contributed to increased out-migration and the eventual extinction of those who stayed behind. Today, the island is an autonomous territory of Denmark, and is populated mostly by Inuits -- whose ancestors date back to the time of the Norse settlements, but who were much better at inhabiting the place.
Bottom line: Greenland was always covered in ice throughout recorded history, though it is possible that throughout the centuries there may have been some variation in just how glacial or green it's been.
The key exchange comes at the 23:00 mark: