The shutdown command has already an embedded scheduler so you don't need a cron job for it to run at the specified time. In Linux as everywhere else, it's better to stick to the KISS principle (Keep It Short and Simple).
shutdown -h 22:00 will work fine, no need to run it in the background. Add the command at the end of /etc/rc.local (or /etc/rc.d/rc.local depending on your system) for execution in the last startup script.
The advantage of not using cron is that in this way the shutdown remains scheduled during the day, and you can cancel it at any time by typing
shutdown -c