Thunderbird doesn't have a built-in option to minimize it to the system tray. But there are some third party utilities with which you can do this. One such nifty utility is Thunderbird-Tray.
* Ater installing Thunderbird-Tray, it sits in the system tray. You can launch Thunderbird.
* Now, when you minimize Thunderbird, it will minimize to the system tray instead of the taskbar. The context menu also gives an option to instantly compose an E-mail message