Read the linked article. Email clients wrap the contents of forwarded messages in a <blockquote>, you just have to use CSS rules to hide the contents of a "blockquote yourfooterclasss" while otherwise showing yourfooterclass by default.
EDIT I actually meant "read the article linked from the linked article" — I too spent a good minute there trying to find out their solution.
It varies between mail clients, but they generally put the forwarded part of the message in either a blockquote or a div with a class that can be targeted. It's how the vertical blue line is produced for the quoted portion.
Basically most e-mail clients change the dom structure in some way when you forward an email (like wrapping the original in a div). Write some CSS rules that require an unmodified structure to show the unsubscribe button.
EDIT I actually meant "read the article linked from the linked article" — I too spent a good minute there trying to find out their solution.