If the symptoms are from the neck up (stuffy, dripping nose, head cold, etc) then it is ok to train. If the symptoms are from the neck down (lung congestion, body aches, fever, etc) then it is best to lay off.
Once I did not follow this adage and ran when I had chest congestion and ended up giving myself pneumonia which put me down for a much longer time than if I had just laid off for a couple of days.