There are forests in the north but not really in the same sense as in other countries. The forested areas are neither natural nor large. We have natural birch tree growth, I suppose you could call some areas quaziforested. That being said Hallormstaðaskógur can be pretty, as well as Vaglaskógur. (Link to a song about a springnight in Vaglaskóg)
Well, naturally, Iceland got almost completely deforested during the Middle Ages. AFAIK, the current woods (well, groves