Here are some tips for dressing appropriately for Iceland's weather:

1. Check weather statistics before you go. Know what the best and worst weather could be like.

2. Snow becomes rain and slush when it melts, so wear waterproof clothing and boots.

3. Take layers of clothes, although even hotels and buildings never seem to get hot.

4. Take or buy snacks if you are going on excursions for hours on end, particularly night time - ie Northern lights tours.  Even in late March there is snow, freezing conditions, rain... You will NOT have a good time if you are not prepared. 

Be aware that windproof clothing is ideal if it is breathable. At the very  least, spray your hardest wearing trainers with waterproof spray and take it with you! Take lots of socks, gloves, hats. Ski-ing goggles would be ideal for night hikes and excursions to stop your face from freezing too. Try taking a flask for hot coffee or chocolate.