You bet. The default formula for the field bound to the textbox would be:
substring-before(fieldwithdate, "-")
XML stores dates in yyyy-MM-dd format. The date picker or other control may display the date differently, but if you open an XML file saved from your form and look at the date field, it will be yyyy-MM-dd. If it includes time, it will be yyyy-MM-ddTHH:mm:ss