I wrote the answer as "He does not have a cold"; the answer was accepted but "He does not have the cold" was suggested as an alternative. In thinking about it, I'm not sure why my answer wasn't labeled incorrect; would not the use of "an cnatan" make it unequivocally "the cold"? I would think "He does not have a cold" would be "Chan eil cnatan air"
That depends on where you are. In the rural parts of the southeast US, and especially in Appalachia, you'll hear "the cold" from older natives. The colloquial where I live in the States is "the cold". You'll also hear "the chills" (versus "a chill"), "the cancer", etc.
That area of the USA was influenced by a lot of Scots and Irish settlers dating from the 18th century. Cant think of her name just now, but the woman who "rescued" Bonnie Prince Charlie settled there. She and her husband were tories during the Revolution, later returning to Scotland. She kept choosing the wrong side!
The only time you'd hear 'the cold' in Australia is if it were followed by '... that's going around' or '... that his wife had earlier in the week'. I wonder if 'the cold' is still accepted use in isolated places, because the one virus hits everyone, whereas in more populous places, people may have different versions of the virus?