I don't know exactly what kind of data you are looking for, but a good place to start in the IRI Data Library is with the Global Historical Climatology Network (GHCN) monthly station temperature and precipitation data.
These can be found here:
We also have daily station data for stations around the globe for 1994-1999. Variables include temperature, precip., dew point, winds visibility, pressure, etc., although the available variables and completeness of the records vary from station to station. These daily data are found here:
/SOURCES/.NOAA/.NCDC/.DAILY/.GLOBALSOD/
Both pages give you global maps of station locations. You can use the controls to zoom in on Korea and select the stations you would like to examine.
An additional source of Korean climate data is the National Climatic Data Center (NCDC):
http://lwf.ncdc.noaa.gov/oa/ncdc.html
-- Michael Bell