I think it depends on whether you say "Does he have short hair?", "Has he got short hair?", or "Has he short hair?", all of which are found among native speakers.
Those who form the question as "does he have?", the natural tag question would be "he has, doesn't he?".
Those who use "has he?" would say "he has, hasn't he?"
While those who use "has he got?" would probably say "he has got short hair, hasn't he?".
Similarly in the negative: you might hear "No, he hasn't short hair", "No, he doesn't have short hair", or "No, he hasn't got short hair".
My impression is that bare "has" in negative and questions ("Has he short hair? No, he hasn't short hair.") is least common world-wide. Without an object ("No, he hasn't.") is a bit more common, I think. I think both of those usages are found more often in the UK than elsewhere.