By default all Windows 2003 Servers are configured to automatically install Windows updates and reboot if needed. Typically most servers are set to reboot between 2-4 AM CST. If you would like to modify the time at which your server installs and reboots for Automatic Updates you can follow these steps.
Log into your Windows 2003 Server via Remote Desktop with your administrative login.
Select Start -> Control Panel -> Automatic Updates
You can use the drop down to select the time wish to reboot the server at. Please keep in mind that the servers are in Central Standard Time (CST) and you may need to convert your time zone into CST to decide the optimal reboot time.