Just a few minutes is all the time the body needs to fully respond to the cold exposure. The physiological response includes Vaso-constriction, the release of endorphins, and a drop in skin temperature of around 40 degrees. Being exposed to this level of cold for long periods of time would be dangerous, but as long as you are wearing socks and gloves, 3 minutes is completely safe and all that is necessary to promote the systemic benefit.