Hi,
What format did you save the playlist in? .PLS or .M3U?
It sounds like you used .PLS, which Wiki says:
Microsoft Windows and its software does not automatically detect PLS format and cannot run it. iTunes, Real player, Winamp, XMPlay, VLC media player and Foobar play PLS files without any extra codecs. Windows Media Player classic with K-Lite codec installed does work with PLS format but still will not automatically detect it.
If that is the case, try re-saving it in the M3U format and then you can use in WinAmp if you want.
Regards,
David