The email submit capabilities are strongly tied to the version of Acrobat / Reader that the end user is using. I do not use the webmail features myself, but I know support has recently expanded in the latest versions, perhaps you should check them out?
The "Submit by Email" button enables to submit your form data in two modes.
1) Default Email Application (MS Outlook)
2) Use Webmail
You can use option 2 to submit form data through Webmail.