Another thread described how to change the border color of the control, but I can't figure out how to target the up and down arrow buttons in an IntegerUpDown control and change the brush for the arrows. Is this possible?
Yes, it is possible the arrows inside RadNumericUpDown to be customized. You need to make modifications inside the Control Template of RadNumericUpDown. All visual states of arrows are the visual representation of the ButtonChrome control. I've demonstrated the approach in the attached project. Also I attached the style of the ButtonChrome control so you could easily modify it.