First, you have to enable "Show icon preview" in Finder > View > Show View Options.
I just tried this...
• Right-click on the Facebook icon on the webpage. Select "Copy Image"
• On your desktop, Command-I on the link you earlier dragged to the desktop.
• Click on the ugly paper-looking icon in the upper left corner.
That should give you the icon on your desktop. It'll probably be fuzzy and ugly, though, as you are copying a low-resolution image.