Will my warranty be valid in other countries if I buy an iPad in Korea?
Yes. But with a cost.

From Apple's iPad warranty docs:


  If you seek service in a country that is not the country of original purchase, 
  you will comply with all applicable import and export laws and regulations and be responsible for
  all custom duties, V.A.T. and other associated taxes and charges. Where international service is 
  available, Apple may repair or exchange defective products and parts with comparable products 
  and parts that comply with local standards. In accordance with applicable law, Apple may require 
  that you furnish proof of purchase details and/or comply with registration requirements before 
  receiving warranty service. Resources with more details on this and other matters on obtaining 
  warranty service are described below.