I don't know how easy or hard it will be to be Vegan in Korea, but I do know that living and maintaining a vega diet abroad is not that difficult if you do a bit of research first.
In most countries, there is a staple grain in the diet. It is often prepared in many ways, mostly seasonally. At least one method of preperation is usually vegan friendly. I would make sure to know what that is.
Also, I suspect that in Korea they have a large Buddhist population, some of which is very vegan friendly. Perhaps they have food that caters to vegan buddhists.
Basically, a bit of research will help you. You could even go to a local Korean restaurant in your town and ask what foods are vegan in Korea. In my local Korean restaurant I order kim-chee (spl?) and Be bim Bop with brown rice and tofu instead of egg.
I am sure you will be fine.
-Rodolfo Palma Lulión