My favorite site for icons is Iconomize.com because the icon you choose automatically installs to your desktop with the shortcut already set. They have the facebook icon here, link Just click to install and it goes right on the desktop.
In fact yes you can:First you go in google images and type "FACEBOOK ICONS"and save the pic,then you go and search"www.iconverticons.com",convert the pic into an icon and download it,then go in the desktop:
go to"new","shortcut",type:"www.facebook.com",then name it "Facebook",then right click on the shortcut ,go to properties,change icon and choose the one you converted before,then press APPLY.and then it should come perfect