The light from the moon is dispersed the same way as the sun. But there usually isn't enough light to notice the dispersion the way the sun does. The moon doesn't produce its own light. You are just seeing the light reflected from the sun. Think of it like this. In the dark, you take a flashlight and aim it at a rock looking at the sun would be like staring directly into the flashlight and looking at the moon would be like looking at the rock. Notice how the rock doesn't really illuminate much else with the light reflecting off it.