In Seoul, the capital of Korea, located in the northwest of the country, a short distance from the coast of the Yellow Sea, the climate is continental, with cold but sunny winters, and hot, sultry and rainy summers. Like the rest of Korea the city is affected by the monsoon circulation: in winter the northwest cold currents will prevail, while in summer they will be replaced by hot and humid currents of tropical origin. Spring and autumn are transitional periods, mild and pleasant, especially the month of October.
Here are the average temperatures.
Seoul - Average temperatures
MonthJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)-6-4171318222217103-3
Max (°C)241018232729302620124
Min (°F)212534455564727263503727
Max (°F)363950647381848679685439

In winter, the average temperature is a few degrees below freezing (0 °C or 32 °F); sunshine is quite common, and a cold wind blows from the Asian continent. On colder periods, the temperature remains below freezing during the day as well; in the worst moments it can drop at night to -20 °C (-4 °F).
Although winter is a dry season, sometimes it can snow.
In winter and especially in spring (March to May, which is called yellow dust season) the city can be reached by the yellow dust (HwangSa in Korean), coming from the desert of Mongolia and from China (though in truth there is also a contribution given by local pollution), which forms a characteristic haze and brings breathing problems and eye irritation.
Spring is mild, but the rains increase gradually. The rainiest season, however, is summer, because of the summer monsoon: from June to August, more than 800 millimetres (31.5 inches) of rain fall. The rains can sometimes be torrential. Usually the worst month, the wettest and least sunny, is July. In summer there can also be periods of good weather, which can be very hot, with highs about 35 °C (95 °F) and more.
In Autumn, rainfall decreases, and by October the rains are quite rare. Here is the average precipitation.
Seoul - Average precipitation
MonthJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec.(mm)202545751001353303501405055251345
Prec.(in)0.811.833.95.31313.85.522.2153
Days767891016149797108

From July to early October (and occasionally also in the second half of June), Seoul can be affected by typhoons, the tropical cyclones of South-East Asia, although this area of Korea is less exposed than the southern coast.

Seoul

The amount of sunshine in Seoul is decent in winter, and also in spring and autumn (although it's lower than in the southern part of the country, like in Busan), while it reaches its minimum in July, when cloudy skies prevail (the amount of sunshine drops to 27%), because of the summer monsoon.
Seoul - Sunshine
MonthJanFebMarAprMayJunJulAugSepOctNovDec
Hours566776456655

Near Seoul, the sea is very cold in winter, but it warms up a lot in summer, reaching 24 °C (75 °F) in August.
Incheon - Sea temperature
MonthJanFebMarAprMayJunJulAugSepOctNovDec
Temp (°C)5558131722242319149
Temp (°F)414141465563727573665748