In the UK at least, natty was a complement, if you looked natty, it meant you were smart - Collins English Dictionary says "(informal) smart and spruce (dialect "net" neat)."

Other songs I know with hair references:

Lakes of Pontchartrain - "Her hair around her shoulders in jet black ringlets fell."
Willie Moore - "Her eyes were as bright as diamonds in the night, and raven black was her hair."



(Incidentally, is it a coincidence that the two clicky ads below this message box are for hair loss treatment?)

Splott Man