It would be great to be able to create a new custom field and choose "Date" as the field type. I often find myself importing dates as custom fields when the data that I am importing does not fit nicely into any of the pre-built fields. Some examples are things like "Graduation date" or "Confirmation date" (from a previous email service). Given my current options, I generally opt to use a 'text' custom field, as doing so retains all of the non-numeric characters in my date/timestamp, but this renders the field useless when it comes to filtering. A custom date field would allow me to search for signups who have graduated between two specific dates, for example.
One should be able to import data to this field much like they would import dates to non-custom date fields (making sure to match the MM/dd/yyyy HH:mm:ss.SSS format).
When this custom field input is placed on forms (i.e. when "requesting" custom fields), the input could have the input type "date", which would force a date picker. As for printing out the field, one could use the already existing "date" filters in liquid.