The short date type is dd/mm/yy, so it appears correctly in the form (day/month/year) But in the mail it is shown with month first. (month/day/year)
How can I change the date type in the mail?
Try go to admin/config/regional/date-time and set your site's Medium date type format.
Also, if the Medium format doesn't include at least a month, day, and year field, Webform will default to the American format of MM/DD/YYYY.
Webform uses the "medium" in e-mails and viewing submissions, though everywhere else (like a displaying the date component) it uses short for the order