Is there a way to make Windows 7 do this: "10 minutes from now, close all applications and shut down (or hibernate), no matter what input you get from the keyboard or the mouse"? It's OK if the user can revert the shutdown order during the 10 minute period, but once the shutdown begins there should be no turning back.
There are a number of automatical shutdown programs on the net. You can use one of them; for example: Sweet Dreams.
As Havok stated, you can just use the Shutdown switch from command prompt. See options below.
Run from cmd.exe or just put into a .bat script as below (and you could just add this .bat to Windows scheduler if you wanted to schedule) - remove the "pause" if you want it to run straight away:
@cd / @cls @echo #Shutdown 10min script# @pause @shutdown /t 600 /s