According to the Landnámabók, the first names for Iceland were Snæland (Snowland) and Garðarshólmi (Garðar's Islet after Garðar Svarvarsson, who rediscovered it). The former one is about the same way descriptive as Iceland. The first Scandinavian to intentionally sail to Iceland was Flóki Vilgerðarson. He arrived in winter and waited for spring to return. He was surprised to see Iceland turn green, so the association of Iceland with ice and snow is not a long stretch.

Greenland on the other hand is an intentional misdirection. Icelandic sagas tell us of Erik the Red, who went to Greenland after being exiled from Iceland. He named it Grœnland, hoping to attract more settlers, succesfully.