Can I install a full copy of Snow Leopard on an Apple TV?
Maybe if this is possible, an AppleTV do not have all the hardware requirement for Snow Leopard, as it needs 1G of RAM. The processor is also only 1 GHz (maybe a bit more, depends on your version) and the lowest Intel processor built on an iMac was a 1.83 GHz Core Duo.

So, even if you achieve to install Snow Leopard on your AppleTV (let say you remove the disk, install Mac OS X on it, then plug it in back), it will be really slow.