Jeremy, Rabanito, Eric, Paulo and Francois - thank you.
Eric - Your observation is largely on point. But there are traditional forests of birch, with rowan, tea-leaved willow and aspens thrown. These are trees native to Iceland. All the photos in my post feature these old forests. You just have to go to the right places to see them.
Afforestation efforts in Iceland are relatively recent and don't cover all that much. As a result, you find sporadic patches of larch, Alaska spruce and poplar which have been recently introduced (spruce ruins it for me as it doesn't suit the Icelandic landscape, in my view).
Old Icelandic joke:
Q: What do you do if you are lost in an Icelandic forest?
A: Stand up.
