I came across an article, Color Vision in the Horse by Joseph Caroll (2/13/02), which discusses this phenomenon.

Yes, horses can see color but, not as well as humans. The cone cells in the retina of the eye are responsible for color vision. Horses have dichromatic color vision (two-colors), in which they absorb light maximally in the short wavelengths and the second cone cell absorbs middle to long wavelengths. On the other hand, humans possess trichromatic cone cells (three-colors). Horses can see some color but it is different from the way you see color.

Since horses are active in the day, at dusk, dawn, and night, they have eyes designed to have both high sensitivity for vision in dim light and good visual acuity under higher light levels. But their night vision is nowhere near as good as cats and dogs. Based on an evaluation of the cells in their retinas, as well as behavior tests, it is felt by researchers that horses have the ability to distinguish red or blue from gray easily. Their ability to differentiate yellow from green is not as good. Beyond this, testing for color vision is difficult.