Considering its northern latitude, Denmark has a fairly mild climate all year round. Still, the winter months - cold and with short daylight hours - are certainly the least hospitable. Correspondingly, many tourist destinations come alive in late April, when the weather begins to warm up and the daylight hours start to increase, and by October they again become sleepers.
May and June can be delightful months to visit: the earth is a rich green accented with fields of flowers, the weather is comfortable and you'll beat the rush of tourists. While autumn can be pleasant, it's not nearly as scenic because the rural landscape has largely turned to brown.
High tourist season is July and August. There are open-air concerts, lots of street activity and basking on the beach. Other bonuses for travellers during midsummer are longer hours at museums and other sightseeing attractions. The last half of August can be a particularly attractive time to travel, as it still has summer weather but far fewer crowds.
