More InputDate Customization
You can customize the icon shown in the drop-down button by changing the InputDate's controlTemplate property, or by using code to change the control content. The first option would affect all InputDate controls in the application; the second would affect only a single control.
You can also customize the format used to display the current month/year in the drop-down Calendar by changing the Globalization's standard 'y' format, or by using code to change the control content. Again, the first option would affect all InputDate and Calendar controls in the application; the second would affect only a single control.