how can I use the shutdown command to hibernate the computer in X hours?

The -h switch is used to shut down the computer on Linux, not Windows. The correct command to shut down a Windows computer after 7 hours is:

shutdown -s -t 36000

Windows will show a dialog box with a countdown until the time the computer will shut down.

But, you want to hibernate, not shutdown, and unfortunately, the /h and the /t switch don't work together. As a workaround, you can use the at command to schedule shutdown /h to run at a certain time. For example, it is 3:00pm in my time zone at present, so 10 hours later would be 1:00am. To schedule it to hibernate then, I would run:

at 1:00 shutdown /h

It uses 24-hour time notation, so if you wanted it to hibernate at 1:00pm, you'd run:

at 13:00 shutdown /h

Please note, that while you don't need administrator permissions to run the shutdown command on default Windows installations, you do need them for the at command.

It doesn't look like the -t option is supported with the -h option for shutdown.

Under Windows 7, you can duplicate what you're trying to do with a .bat script containing the following:

timeout /t 36000 /nobreak
shutdown -h

It will cause the PC to immediately hibernate once timeout is done counting down.

PsShutdown from Sysinternals can hibernate the computer after a specified amount of time.

psshutdown -h -t 36000