In Glasgow in the the 1960s a 'Hairy' had come to mean a working class female who was regarded as a likely respondent to sexual overtures.
However, I understand that the origin is after the first world war when many more females were in the workforce. 'Hairies' were those working class girls who did not wear hats. There's a reference to this somewhere in 'No Mean City', which is much derided by Glasgow folk as unrepresentative, but was still pretty accurate when I was growing up in the Grobals during the late 50s and early 60s.