Winamp skins were surprisingly restrictive, though; you couldn't really skin Winamp in a way that impeded its functionality / created mystery-meat navigation. Every Winamp skin was fundamentally just a set of textures applied to the same standard controls layout: https://skins.webamp.org/
That was true for "classic" skins, but starting with Winamp 3, Winamp supported free form "modern" skins that were defined in XML and had a custom scripting language so that the author could define their own behavior.
True; though I'm pretty sure the WinAmp anyone here actually has any level of nostalgia for, is WinAmp 2. WinAmp 3 was so lacklustre that they brought back a lot of WinAmp 2 stuff and called the result WinAmp 5. (And then everyone continued to use the Classic skins, which WinAmp 5 supported.)
Windows Media Player, meanwhile... https://www.theskinsfactory.com/wmpdesign