Is it possible to use a drop down menu with images?

Another option is to mimic a drop-down using buttons with images. One can be the trigger to show all the options, and the others will "close" the menu when clicked and store the selected value somewhere.

This will require the development of a custom-made  script, though.

No, but you could make a workaround, by using dropdown field with labels and create hidden image fields and then show/hide them depending on what you choose from dropdown.