In Mountain Lion, Apple replaced the webarchive format for signatures with a new format .mailsignature.
STEP 1: In Mail, go to Preferences > Signatures and create a signature with any random content. Name it something meaningful. You will be swapping this out later.
STEP 2: Write an HTML page inside of your favourite text editor. The page should not have HTML, head or body tags but should include only inline CSS and basic HTML elements.
STEP 3: In Finder, go to Go > Go to Folder and type in ~/Library. All your email signatures should be inside Mail/V2/MailData/Signatures.
STEP 4: Locate the file you created in Step 1 using quick look (spacebar).
STEP 5: Replace the content between tags in your mail signature with the HTML you created in Step 2.
STEP 6: Quit Mail and then right click the mail signature file in finder and select ‘Get Info’ then tick the ‘Locked’ checkbox. This prevents mail from resetting the file to the original version and it uses your version.
That's it. You now should have your new email signature working with Mountain Lion.