Winamp is fine with HTTPS addresses.
It uses the components of Internet Explorer to display web content.
If the page will not work in IE, it will not work in the Winamp browser.
Any sites that use flash or other plugin will still need it.
The music services I have pasted here do not integrate with Winamp properly, because they do not use the Winamp API.
They are just the most convenient streaming sites I found that functioned.
Some do offer direct links or playlists so you can use play them in Winamp properly.
I should look for others that use playlist files, or have direct links to the files.
These will be automatically opened by Winamp if it is set to handle them.
Mostly it is radio streams that use playlist files
Last.fm may become useful again, but for now I am sticking with Seesu.me.
This can at least create m3u playlists for use in Winamp