"Cold" wouldn't be an all-encompassing word that I would use to describe myself. I'm not malicious, but I can be detached from what's going on, and I can step outside of situations. There may be a point when I don't entirely care about someone's situation, if they blow things out of proportion, and are constantly complaining about it. There is a certain amount of reservedness that goes into it, and not knowing how to react to emotional situations in the moment, and staying out of it, or saying nothing, while still observing. I'm more or less the opposite of cold as a person. I do care deeply for other people overall though.
Some people may perceive me as cold, or rude, or at least having an aloof quality if I don't know them well, and I'm in a setting with a group I am unfamiliar with. I'm a person who it takes a long time to get to know, and meeting me for the first time, people assume. It comes more out of a place of awkwardness, than malice. I can have a sense of detachment when it comes to certain things, but I do feel deeply. I am reluctant to get on the deep level with people.