If you are going when there is snow on the ground, you must be a snow bunny. Just remember winter boots, winter jackets, spikes for the glaciers, etc.
If you are going when it is over 40 degrees Fahrenheit:
Sneakers or boots for walking around Reykjavík
Winter jacket for the rainy/cold days
Rain jacket for the rainy days
Bathing suit for pools/lagoons
I only brought one backpack with me on this trip because we were only there for a long weekend. You can get away with wearing the same long black leggings.
If it's raining season, make sure you have waterproof gear.
LAYER LAYER LAYER!!!!!