South Korea has four very distinct seasons, and the time of year makes a real difference to what you experience.
Spring (April–May) is arguably the best time to visit. The cherry blossoms typically peak in early April, beginning in the south and moving northward. The Jinhae Gunhangje Festival near Changwon — one of Korea's biggest — draws enormous crowds to see over 350,000 cherry trees in bloom. Temperatures are warm without being oppressive, and the countryside looks beautiful. One warning: spring can bring yellow dust (hwang-sa) blowing in from the Gobi Desert, affecting air quality for a week or two at a stretch. Most pharmacies sell face masks.
Summer (June–August) brings heat, humidity, and the monsoon. June and July are the rainy season, with heavy and persistent downpours. August is hot and humid, typically around 30–35°C, with the occasional typhoon. The beaches come to life in late July and August, when Koreans descend on Haeundae and the east coast in huge numbers. It can be fun if you embrace the crowds; if you want solitude, this is not your season.
Autumn (September–November) is the other great time to visit. The skies clear, the humidity drops, temperatures are pleasant, and the mountain forests turn spectacular shades of red and orange. Seoraksan National Park is particularly renowned for autumn foliage and gets crowded on weekends as a result. October is a good month to combine hiking and sightseeing.
Winter (December–March) is cold and dry. Seoul temperatures regularly dip below freezing, and the mountains can be properly arctic. But winter has its pleasures: ski resorts in the mountains, the soothing ritual of the jjimjilbang (sauna and bathhouse), and far fewer tourists at the palaces and temples. Pyeongchang, host of the 2018 Winter Olympics, has the best skiing.