I stayed in Busan for a few months in the early 90's, and my golf-crazy friends made me play in March. The water hazards were still frozen, so I lost fewer balls - they'd hit, then bounce to the other side and onto the land again. I still had to take a penalty when that happened, though.
It shouldn't surprise anyone that there are trout in Korea. They are apart of the pacific rim and certainly far enough north for their waters to hold trout. Our men that served in the Korean War will tell you that it gets cold there.