As far as I know, there's no way, using the limited interface OWA provides, to set outgoing mail to default to plain text. OWA is an active server page shadow of the full Outlook "fat-client", hosted by Microsoft Exchange, that uses an IIS web server for presentation and authentication offering a user only limited control.
I understand that Exchange 2003 -- or, more to the point, the OWA interface Exchange 2003 provides -- gives the user a wider range of control options. The OWA 'look and feel' more closely mimics the full featured Outlook client. I haven't had a chance to deploy and troubleshoot MSEXCH 2003 yet so I'm not certain these claims are true.
In any event, I recommend reviewing the following Microsoft documentation regarding customizing OWA:
Orig URL -
Condensed URL -
http://makeashorterlink.com/?M28E42F68
It may be that some tweak is available -- most likely on the server end -- that your admin can apply to default your messages to plain text.
.d.