Display favicon for PDF files

If you put a favicon.ico to the root of your site, then your PDFs opened on that site will actually have that favicon. You can generate transparent ICOs from PNGs with online favicon genereators.

For example, if your favicon is reachable in:

http://example.com/favicon.ico

Then your PDF will show this favicon in the Acrobat plugin tab:

http://example.com/something/something.pdf

If you show the PDF file in an iframe, the browser should show the site-wide favicon, but you're out of luck in an external applications. Acrobat Reader doesn't use Favicons.

UPDATE This is now possible by placing favicon.ico in the root directory of your website as per @s1m0n1stv4n answer below