Article now on the official Mozilla support site: https://support.mozillamessaging.com/en-US/kb/what-winmaildat-attachment
Microsoft in their eternal quest for a competitive edge just will not stick to agreed standards. This applies to mail as much as it does to anything else they make. Microsoft calls in Innovation, and if you exclusively use their products it certainly can appear that way. It is only when you have the temerity to use a non Microsoft product do you find that their innovation is not compatible with, well anything else really.
This is the case with the winmail.dat file. It is a proprietary format for sending email attachments that only Microsoft programs really understand. Others have spent their time and effort to try and get their programs to understand this format, decode it and present the content in a useful manner, but the Truth is that the problem is outlook.
This article on the office web site advises Outlook users how to fix the problem permanently. Whenever you get one of these messages the best approach is to reply to the message sender that they have outlook incorrectly configured to send Internet mail and give them the link to the article on the office web site. Most people simply don't know they don't have Outlook set correctly and will change things as soon as they hear that your can't open their attachments.
There is an add-on for Thunderbird which in some cases can read these winmail.dat files. Lookout is not always successful, but it can usually display the attached files.