You can apply for one of the phones on the KTO website http://kto.visitkorea.or.kr/eng.kto starting in late February.
The Korea Tourism Organization is teaming up with Samsung and SK Telecom to offer free Galaxy Note 5 phones to "select" visitors coming through Seoul's main airport (about 250 per week) for up to five days.
You only get 1GB of data, but that beats paying through the nose for international roaming or local prepaid service.
I wonder what you'll be liable for if you lost the phone?