I think the root for this confusion is well explained in this wikipedia article.
While the IANA-registered MIME type for ICO files is image/vnd.microsoft.icon, it was submitted to IANA in 2003 by a third party and is not recognised by Microsoft software, which uses image/x-icon instead.
If even the inventor of the ICO format does not use the official MIME type, I will use image/x-icon
, too.