The climate in South Korea in March is going to be cold and generally harsher than winters in the UK. The later in March you travel the better the weather will generally be however.
March is still a cold month in South Korea and there still may be some days where temperatures drop below freezing.
Temperatures in Seoul tend to be a little higher than in the countryside, purely due to the concentration of buildings and people which help to maintain warmth in the urban landscape. March also tends to be quite dry in Seoul.
Temperatures in Jeju Island are on average 5 degrees higher than those in Seoul.