Given the large number of cognitive tests that measure memory and the large variety of achievement tests in use, it's hard to give an accurate figure on how many use color. We do know that many learning materials used in school rely heavily on color, which is a problem for colorblind students. Although I could find no studies that specifically addressed issues related to cognitive test performance and colorblindness, we are starting to see efforts to address colorblindness in a variety of fields. Web designers now routinely avoid problem colors, combine color with graphical elements, and limit the number of colors on web pages to assist colorblind individuals.
People who are colorblind can learn strategies to compensate for the deficiency, and the FDA recently approved new contact lenses and eyeglasses that are effective in addressing the problem.
If you are concerned about how your son's test performance may be affected by his colorblindness, you might want to consult your eyecare practitioner to get more definitive information about what sorts of specific color combinations would be significant for your son. Armed with that information, you then can sit down with the professionals who tested your son to determine whether the tests he took would have hindered his performance.