There is plenty of evidence that zinc has effects on the progress of rhinoviral infections. I don't know of any detailed determination why, but it seems tied up with preferential activation of certain immune system components. People who respond well to zinc treatments often report immediate dizziness after remarkably small doses, when taken as cold symptoms are emerging.

They used to sell a gel that, it turned out, caused permanent loss to sense of smell if snorted (against pkg instructions, but who read those?). Now you find lozenges, which seem to work about as well.