Downgrade Mac OS x


I have a Macbook (old 2006 model) and made the mistake of installing Mac OS X Lion. Now, as performance has obviously decreased, I was thinking on downgrading the OS to Snow Leopard. The question is: can I just install a fresh copy of Snow Leopard (formating the drive)?

All I've read is about downgrading but wanting to keep the files (so I read that you need Time Machine and so), but I just want to erase everything and istall Snow Leopard from the DVD. Is that possible?