Do you have to beat the main game in order to play the "Cold Cold Heart" DLC?

You don't have to beat the game, there will be an Cold Cold Heart option in the main menu. It has its own separate save slots and acts apart from the main game. There are some minor spoilers for the main game but for the most part it is a separate experience. It is very similar to the Freedom Cry DLC for AC4 in how it is structured.

No, the DLC is very much like the Harley Quinn DLC for Arkham City. There's a separate selection on the main menu to start it.

Have both of you beaten the main game before playing "Cold Cold Heart" DLC, or did both of you have played that DLC without beating the main game? I'm just making sure what you guys said is correct.

Haven't beaten the game on PC and the DLC worked fine on PC.

Thanks for info.