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.