If you google "naengmyeon" you'll find a list of websites claiming one and the same—this ice, starchy, spicy buckwheat noodle soup is perfect for a hot summer day, something like that.
Yet in Korea it, in fact, has to be on the contrary, as they follow the principles of the Eastern Asian diet. This diet encourages to eat hot food in hot season, and correspondingly cold food in the cold season.
If you come to Korea for an authentic experience, then it would be relevant to also follow these principles, and eat the cold soup in the cool season. On average January appears to be the coolest month in Korea.