MinimizeToTray Plus is an extension that allows you to minimize an application to the system tray. It currently supports Firefox, Thundebird, Sunbird, Songbird, Flock, Postbox and SeaMonkey for any version based on Firefox 3 and higher.

I believe this is the only MinimizeToTray like extension the currently supports Thunderbird 3

It features include

• Ability to minimize and application using a menu item, toolbar button, or keyboard short cut.
• A tray menu for interacting with the application while minimize (eg.for Thunerbird open compose message).
• An options window for customizing how the extension behaves, options include.
  • Always minimize to the tray instead of to the taskbar
  • Require a double click to restore from the tray
  • Minimize to the tray on close
  • Always show tray icon
  • Restore window instead of opening new
  • Only ever show one tray icon
  • Load application at system startup
• A command line flag -tubo for starting the application so that only the tray icon is visible.

Some of the uses of the application might be to hide Thunderbird, while it still check for emails. Or Sunbird while it still shows alerts. Or simply to keep the application running in the back ground to it "starts" faster. Among many other possible reasons for using it.