With a location on the Arctic Circle, the only sensible time to visit Iceland is during the summer, when you get sunlight and tourist attractions are open. There are many festivals - particularly around midsummer, when there are parades and parties throughout the 24 hours of daylight.
Travel to Iceland during the winter is possible, and you tend to get very attractive deals on hotel accommodation, although there is not so much to do outside Reykjavik, and it is very, very, very cold, and awfully dark throughout most of the day.