Icelandic ships were almost exclusively built elsewhere and sailed to Iceland (e.g., Norway and Denmark). No viking era ship has been found in Iceland and there is no evidence that any substantial number of ships capable of traveling between Iceland and Scandinavia or the British Isles (if any) were in Iceland. We assume that those found in the countries of origin for the ships that traveled to Iceland were made if the same materials.

The Roskilde Viking Ship Museum in Roskilde Denmark is an excellent source for info on boatbuiding materials and techniques during this period. Their book, "Archaeology and the Sea in Scandinavia and Britain" has rather extensive discussions on wood types. Ash and oak are highlighted in early Scandinavian boatbuilding. The Hereby I longship found near Roskilde is described as, "built from radially split, large, high-quality oak planks up to 10 meters in length." The Skuldelev V was constructed of 4 woods. The vast bulk of the hull was oak. Small portions of the upper planking (near the oar holes and slightly below), were make of pine, alder and ash in descending order of use.

These are just representative samples, but they give you the idea. I cannot find any references to the use of driftwood to build or repair ships, although it is impossible to rule out that someone in this era may have repaired a ship with solid driftwood in a pinch. Repairs are a common find in "viking" ship excavations and help scholars estimate the age of the ships.