The North didn't win. The Korean War effectively began when the North invaded the South and it ended with an armistice. The North had not achieved its objective (to unify Korea under North Korean rule), and the end result was an exchange of territory that was relatively equitable.

I see two defensible claims that might be made about the Korean War:

1. Nobody really won because it ended in a stalemate and the conflict persists to this day.

2. The South/UN/US won because the North was kept from achieving its goals.