This question doesn't duplicate the more limited one on Zicam; I ask here about zinc in general.
Since then, research has turned up mixed results about zinc and colds
For many years, it has been suggested that zinc supplements could relieve the symptoms of the common cold, but there was little clarity until a 2011 evidence review. This recent review suggested a modest reduction in the length of symptoms, although the results were not entirely conclusive. In a bid to help clarify the matter, researchers have conducted another review of evidence on this issue.