Exclusively in Winter.
Iceland in Winter, there is interesting itinerary to see more than the northern lights. It is the ice caves that situate at the edge of glacier. You have to book a guide tour because it is too dangerous to enter the cave yourself. You have to do it only in winter because the warm weather would make the cave collapse.
After visiting one of the Ice Cave in Iceland last year, I made a visit again in mid February. This year, during my trip, the temperature was to warm to visit some beautiful cave.