Iceland is plenty icy enough on its own. Lots of glaciers. But instead of covering 99% of the island, like Greenland, it's just a significant portion of it, instead. Also the weather there isn't particularly warm or great, even if it's more hospitable than Greenland
I went to Iceland for a trip in very late December. It's decidedly not green in winter.
Tomorrow is going to be the first snowy day in Reykjavik this year.