How do I change the font size and color in an Excel Drop Down List?

Unfortunately, you can't change the font size or styling in a drop-down list that is created using data validation.

You can style the text in a combo box, however. Follow the instructions here: Excel Data Validation Combo Box

You cannot change the default but there is a codeless workaround.

Select the whole sheet and change the font size on your data to something small, like 10 or 12. When you zoom in to view the data you will find that the drop down box entries are now visible.

To emphasize, the issue is not so much with the size of the font in the drop down, it is the relative size between drop down and data display font sizes.