Cheese in the Trap - This ML is so cold that he's essentially sociopathic, although he hides that aspect of himself from most people pretty well. The FL sees through it, which catches his interest.
Eternal Love - The ML is pretty stoic.
Liar Game - The ML is cold/stoic most of the time, but there's not much in the way of romance. It is hinted at, at most.
My Girl - The ML is introverted and can often seem cold, but he's actually gentle and warm-hearted.
My ID is Gangnam Beauty - The ML is introverted no matter who he's with, and fairly cold unless he is interacting with his friends or love interest. He can even be kind of cold with his best friend.
Princess Agents - Both MLs are cold in their own way; Yu Wen Yue has a cold personality but he is actually a kind person who is sometimes conflicted by his responsibility to his family/household. Yan Xun is initially a outgoing, sunny character who experiences an extremely traumatic event and changes dramatically as a result.
Suspicious Partner - The ML is introverted and can be a bit cold/crabby.
The Last Empress - Wang Shik has a stoic disposition and only becomes a bit warmer around the FL. Lee Hyuk can be cold, but he's also childish/goofy and funny in many scenes later on.
Touch Your Heart - Lee Dong Wook's character is pretty similar to his character in Hotel King (and My Girl).
You Who Came From the Stars - I didn't love this one, but many drama watchers are fond of it, and the ML is very stoic/cold most of the time.