Outlook has only one date and time related feature in email messages.
As you may know, Outlook’s email editor is really Microsoft Word with limited features.
On the Insert tag there’s a Text | Date & Time option which opens the same dialog as in Word.
Update Automatically inserts a field code, just like in Word. Right-click on it to see the same, very useful, options.
Update Field changes the time displayed.
Toggle Field Codes displays the {DATE} field. It gives you the option to change the formatting beyond the limited choices in the dialog box.
What happens when you send the message
The DATE field is updated when you click Send and converted to plain text for the outgoing message.
The outgoing message has nothing to indicate that the date/time was a field code. Your copy of the sent message (in Sent Items) is also plain text without the field code.
