I know you are not using Microsoft Outlook as your email client program, since this wouldn't be a problem if you were using it.
One solution to the problem is to visit
http://www.biblet.com and download the WMDecode program found there (look about halfway down the page). This will at least allow you to decode the winmail.dat files and extract any useful attachments from them.
Other than this, there's not much you can do on your end to fix the problem, since it's not your email program generating the problem. If you just don't want to deal with the problem, the other approach is to reply to the individual who sent you the offending email and ask that they re-send the message, with the attached files, as a plain text message, not in Rich Text Format or HTML