Green’s Dictionary of Slang

winnie n.2

[? the female name or his ‘whinnying’ tones]

(gay) an effeminate homosexual man.

[UK]L. Durrell Black Bk 168: ‘He’s a kind of pansy,’ she remarked. ‘I don’t like it. I seen that kind before. He’s a winny’.
[US]B. Rodgers Queens’ Vernacular.