Think layering, and do not forget the hat . Note that the excellent and colorful Icelandic sweaters are cheaper in Reykjavik than abroad, and these are top-quality insulation for Icelandic conditions. Ski socks are best, excellent with lighter under socks. You will want dry feet, and 6-8 pairs will usually do this. Rubber boots for wet days and work or hiking boots for other times.
Slippers can be useful for in-house wear.
Think old and sturdy. Iceland has Scandinavian prices.