Hugh, I believe that Iceland had forests in the past.
It consisted mostly of birch and osier and covered perhaps 60% of the surface. That was around the year 900.
Before the end of the Middle Ages north Norwegian settlers used it up and the sheep they brought finished the remains and the sprouts.
There exists an old report already stating the devastation.
See 'Reise igiennem Island' , Eggert Ólafsson, Bjarni Pálsson, Danmark, 1772.
Today there are initiatives, private and public, for reforestation.
23 - 11 no trees here
23 - 12 crown of the day