The reason why this is an argument is that "Head Cold" is too broad a term...
As I'm sure we've all experienced there are a variety of symptoms from a runny nose through aches/pains/headache, raised temperature or fever, catarrh, blocked eustachian tubes, earache and varying degrees of malaise; being human we are all different in our response/symptoms to each cold we get.
Every Pilot, before every flight, needs to address the IMSAFE mnemonic and as part of that ask themselves if fit to fly.... minor symptoms at the start and end of a head cold may not be a problem but fever, general malaise and blocked or infected eustachian tubes/ears will almost certainly require the pilot to postpone/cancel.
Mike