Summer and winter are the most popular seasons to visit Iceland. Visiting in spring can be a clever idea if you want to avoid the crowds. Prices tend to be a bit lower during the shoulder seasons too, so that's also one of the upsides of visiting in the spring.
In my opinion, spring is the most delightful season in Iceland. The days keep getting brighter and there's a sense of optimism in the air. In early March, the evenings are already bright. A lot of tours and excursions in Iceland operate only from May to September, but I've picked the best tours that operate during the spring months.