It’s always important to be ready for any kind of weather, all year round. Knowing what to wear is more important then the amount of layers you wear. Quality over quantity!
All Icelanders own wool clothing, it’s the best material to fight the cold. Föðurland or the “Fatherland” are thing wool pants you wear under your normal pants, it’s a mush have in Iceland. Below you will find some recommendations.
Putting on many layers of bad material is not going to help you much on a cold day. Having a thing wool layer under your clothes and a big, warm, waterproof coat on top is all you need. +scarf, hat and gloves.