Perhaps we are unusual, but we have some legacy domains in Exchange from corporate acquisitions, as well as SmarterMail for our primary user base.    Since upgrading to MAPI-enabled SmarterMail, we have been having problems with some messages from Exchange domains arriving into SmarterMail with Winmail.Dat attachments.   Some web articles leave the impression that this will only happen if the user message is prepared in RTF format, but this is not correct.   Our problems occurred on HTML-formatted messages with attachments.   One web article said, apparently correctly, that TNEF contains supplemental content which only Outlook understands, and it can be attached to base messages with any format.

I remember reading, a long time ago, that the actual processing depends on Exchange believing that the target system is another Exchange server, as well as the message formats.  So apparently SmarterMail now successfully mimics an Exchange server.

Another web search provided the global solution.    In Exchange Management Console, navigate to Organizational Configuration...  Hub Transport... Remote Domains.   Open the properties window for Default or another object.   From the Message Format tab, change "Exchange rich-text format" to "Never use"