It seems that the range search field does not work with dates. Even if I define a upper/lower bound it is not possible to define more than one date in the search field. In the documentation I cannot find anything about it. Maybe I overlook something or cannot find the right separator. Ideas are welcome :)
Create two search fields of the same date attribute. One with the greater then and one with the lower then properties. When you fill out both fields you have your date range.
Ronald's solution is the way to go. In case you're wondering what that range search filter does, the following page may come in handy