How vulnerable is 10.6 Snow Leopard to hacking? My 2007 Mac Mini is used as a TV media device, for watching free-to-air TV channels and Youtube. It cannot be upgraded past 10.6.8.

I read somewhere that older OS X can be vulnerable to unnoticed outside hacking, cannot find the reference anymore. Is this so? Is there a way to detect?
Yes, there's a variety of exploits available. Though there's no one complete list, there's certainly a variety (see this one), including Shellshock, a remote exploit in Bash, and SeaPea, a root exploit. Apple will not patch these issues, as Snow Leopard is no long supported in any capacity.

While if you're careful, Snow Leopard isn't the end of the world, if you're concerned even remotely about security, given your use case of TV and YouTube, it probably makes more sense to just load up Windows or Linux and roll with that.