How to drop the external source output voltage using Arduino
You're going to want to use some sort of transistor and do pulse width modulation (PWM) from your Arduino. If your LED array is drawing a significant amount of power (or the fact that it's at 10 VDC) you might need to use what's called a Darlington transistor, which is essentially a pair of transistors where the first amplifies the input for the base current of the second one. Here are a few examples using both a FET and a transistor.