This article obliquely mentions the sheep problem but only by saying:
Mr. Jonsson and his volunteers then plant the appropriate species for the plot — birch, Sitka spruce, lodgepole pine, Russian larch or other species. “We’d love to plant aspen,” he said. “But sheep really love aspen.”
Sheep may love aspen but they will eat all the other trees also. I did not realize this was the main reason there was only grass everywhere until, when up on top of the Skógafoss waterfall, there was this[1] little island in the river covered in a little mini-forest. This rocky island would not be a very good place for trees to grow compared to the nice soil under the grassy fields around it, but since nothing could graze on the island, the trees could grow up.
[1] https://njarboe.com/iceland/IcelandTreeIslandSkogafoss.jpg (The trees on this island are only about 4 feet tall)