For normal humans, color is experienced as tri-stimulus values for the three different color receptors in the eye. But this can be broken down into hue, saturation, and intensity, and you could argue that only hue is "color". Hue is measured in the 1-sphere, so is 1-dimensional. If you include saturation in your color, to distinguish a pinkish grey from blood-red, then color is 2-dimensional. If you also include intensity, you get a 3-dimensional color solid.
But that's all about the experience of color. Actual objects have reflection and absorption spectra, which are very high-dimensional.
