While visiting Iceland, I learned that only one percent of the country's original forests still exist. It occurred to me I might be able to return there and plant trees in exchange for room and board, so I posted the question at Iceland Review Online. Thanks to the assistance of Eygló Arnarsdóttir, here's the answer I got:
Thröstur Eysteinsson, division chief of national forests at the Iceland Forest Service, said it isn’t correct that only one percent of the country’s original forests are left: it is approximately five percent.
Today, one percent of Iceland is forested while 30 percent of the country was forested at the time of the settlement around the 9th century AD.
Even though this happened centuries ago and Icelanders have gotten used to living in a forestless country, this is still a serious matter, Eysteinsson said; it is among the most extensive cases of deforestation in the world.
If you would like to learn more about forestry in Iceland and the country’s treeless state, here is a link to an article in English by Eysteinsson on this subject.
Eysteinsson said he didn’t know of anyone offering an arrangement where travelers can plant trees in exchange for food and board.
However, there are a few volunteer organizations that execute environmental projects in Iceland, including reforestation, such as SEEDS, for example.