There are lots of trees in Iceland ! However, they are not seen on the scale that they are in most European countries. Also they are usually quite small and not as vigorous as in Europe. There is a theory that the first settlers on Iceland cut them down to make boats and shelters and they have never really re-established. But it could have more to do with the climatic conditions and the fact that they never really re-established after the Ice Age.
The climate is harsh and the winds are quite strong which can batter young trees. Moreover, the predominance of salt lashing in from the sea means that trees can only grow in selected areas (Iceland is after all an island, so they would have to grow inland).
In the UK, the Shetland Islands (and Orkneys) also have extremely few trees for the same reasons as Iceland, even though they are further south.
The climate is harsh and the winds are quite strong which can batter young trees. Moreover, the predominance of salt lashing in from the sea means that trees can only grow in selected areas (Iceland is after all an island, so they would have to grow inland).
In the UK, the Shetland Islands (and Orkneys) also have extremely few trees for the same reasons as Iceland, even though they are further south.