You are correct, if you close Winamp while minimized it will open minimized.
That's Winamp's default behavior
... you can get around that if you want to.
How do you open Winamp? Via a shortcut?
- Right click on the shortcut
- Select 'Properties'
- Set 'Run' to Minimized
Now when you start Winamp via that shortcut it will open Minimized
(regardless of it's state when closed).
I'm sure there is a cleaner way to do this ... DrO has a number of plugins that deal with minimizing, perhaps it would be logical to add this feature to one of them: