You would have to create a custom field to do what you want. If you look at the HTML source code, Formidable Pro's date field is not a date field.it is a text field that uses the jQuery date picker. When stored in the database, all fields on the form are stored as text or serialized arrays.
You have two choices, create a custom field so it appears on the drag and drop field menu, or create a field in a custom HTML. The second option will not save the field to the database, so you have to transfer the content to a hidden field. The first option requires you to convert the text data in the database to a date using jQuery when displayed in the browser.

hey, thanks for your reply. i have implemented this with the custom field solution and it works quite well. However, there is still one small point to clarify. When I send the form, this format is displayed in the date field in the email: YYYY-MM-DD . However, it should be displayed like this: DD.MM.YYYY
Do you know how I could solve this? The date format is already set correctly in the general formidable settings, but apparently this does not apply to the "custom-date" field.