Upvote:5
You'll find several small forests in Iceland, Hallormsstadaskogur in the East. Vaglaskogur in the North and Baejarstadaskogur in the South. More importantly there are several very large nature reserves where grazing is limited.
Take a look at Nordic Adventure Travel.
Skaftafell is quite well known.
Upvote:6
Based on limited personal experience. I haven't seen all Iceland myself, but from what I've seen it doesn't look like there is anything left what one could reasonably consider a forest. At least not by European/American standards.
When being on several guide tours I also heard there are a couple of very small forests coming from reforestry projects. Those forests are indeed all fenced to protect from sheep grazing, but those are relatively new and therefore small.
As a side note, there is more sheep than people in Iceland (according to my tour guide), and people had much bigger impact to the natural vegetation (according to the same source).