I've read that Iceland used to have up to 40% of its landmass forested, but over the years of habitation it dwindled to near nothing. I imagine that an economy so thoroughly dependent on fishing and ships in general would be hamstrung without a supply of lumber to build and maintain their boats.
The first thing to note is that there was a distinction between timber and choice timber. For smaller items they could use driftwood, or repurpose old wood. Choice timber was imported, primarily through Norwegian merchants and was used for timber buildings and boats. Many homes in Iceland were not wooden, but made with turf, specifically because of the lack of availability of suitable wood. Hastrup has highlighted that Norwegian merchants seemed to have been exempt from docking fees, unlike other Scandinavian merchants, likely due to a treaty very early in Iceland's history. This led to a Norwegian mercantile dominance. Thankfully, the Icelanders initially had a plentiful supply of whale goods such as oils and ivory to export.
As time went on, the situation did worsen economically and it was one factor (amongst many) that led to the Norwegian annexation of the country in 1262/4.
Sources:
OP, where did you read that Iceland once had 40% forested land? And how was that calculated?