Tasker is an Android app that lets you specify "contexts" (specific states of the phone), and carry out actions depending on these contexts. An example use-case might be something like "when I am connected to my home WiFi network, disable my screen lock".

One of the actions available under Tasker is "Run Shell", which lets you issue shell commands to the underlying operating system. To achieve your desired effect, you could:

• Acquire Tasker (a few dollars)
• Set it up to run with root privileges
• Set a context of "between 11pm and 6am"
• Set an action of the shell command "su -c shutdown -h now" (or something similar) to run under that context

This does seem quite hazardous, though. If an emergency happened at 3am, I'm pretty sure I'd want my phone easily available and usable.

ETA: I just Googled to see if there was an existing recipe for this. It turns out Android doesn't have a conventional shutdown terminal command, but does have the "reboot" command, with the switch -p for powering down. Tasker also has a "reboot" under System->Misc, with a power-down option on rooted phones. This can absolutely do what you want it to do. Just don't go having any emergencies between 11 and 6.