A "cold in the head" or head cold in humans is an alternative wording for upper respiratory tract infection. Upper respiratory tract is roughly all the stuff from the throat to the nose, but not the trachea and lungs. This causes all the usual symptoms of being bunged up: drippy nose, maybe a cough, maybe a bit of a fever, maybe a bit of a sore throat. Usually caused by a virus so antibiotics are useless unless a secondary bacterial infection muscles in on the action. Who was it who used that term in relation to a horse? If it was your vets, they were probably being helpful in giving it a name that people can relate to. If it's your horse that has it, just treat him the way YOU would like to be treated if you had a head cold, ie sick note (no work), warm bed, plenty of fresh air, light meals little and often, tlc, understanding and good nursing. A virus can take a surprisingly long time to fully clear but if the horse seems to get worse or develops other symptoms, then get the vet again.