Can I install a full copy of Snow Leopard on an Apple TV?
Solution 1:
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.
Solution 2:
I'm pretty sure it wouldn't work "by default" (i.e. without a kernel and bootloader hack). You might be able to run it using OSx86, but I'm really not sure.
Like Studer said, even if you achieve to install Snow Leopard on your Apple TV, it will be really slow.
Solution 3:
In addition to my rant answer, I took a look at this thread and did a little skimming. Sounds like Snow Leopard is not supported due to some unreleased kernel headers. Not sure why that would matter considering Snow Leopard runs on unsupported x86/64 hardware, but there it is on page 8 from some people who obviously have spent a lot of time with this.
So it would seem that there are software issues in addition to the slow hardware.
HOWEVER, it looks like the aforementioned thread gives quite a bit of practical information on getting Leopard to run! Might be the way to go since Leopard has lower system requirements anyway.