Although 고추 is introduced to Korea only 4 hundred years ago, is spread over all of country very quickly. There are so many kinds of food made with 고추. For Example, Kimchi 김치 has only white color before 고추's arrival.
We Koreans normally eat 고추 in the form of Gochujang 고추장, Gochugaru 고추가루. Sure we eat 고추 as ram one.
As a normal Korean, I cannot imagine the world without 고추. :)