Looking at the literature, I find the following passage in a review of the genetics of colorblindness:
Females have two X-chromosomes, and can either be homozygous or heterozygous for the X-chromosome opsin allele. If homozygous, they are dichromatic; however, females who carry both an allele for an L opsin and one for an M opsin have the equivalent of normal human color vision, having both L and M cones because the process of X-inactivation segregates the expression of the L and M opsin genes to separate populations of cones. The significance of this is that in trichromatic female squirrel monkeys, the difference between L and M cones is solely determined by the stochastic choice of which X-chromosome is retained as the active one. Variation in L:M cone ratio in female squirrel monkeys is similar to what is seen in human males with normal color vision. In squirrel monkeys the variation has been attributed to the stochastic process of X-inactivation, influenced by the number of cells present at the time of activation and other random factors in the inactivation process (Jacobs & Williams, 2006).
Boiling this down: X-inactivation happens at a local enough scale that eyes of heterozygous females have active versions of both normal and mutant opsin genes. So they will still see color "similar to what is seen in human males with normal color vision".
Note of course that people with an XX complement can have better possible color perception than XYs, as they have the potential for tetrachromacy:
females who are heterozygous, for example, having OPN1LW genes that encode two spectrally distinct L pigments, would have four different cone types -- two different L, plus M and S -- and thus the potential for having tetrachromatic color vision (Bosten, Robinson, Jordan & Mollon, 2005, Jordan & Mollon, 1993, Jordan & Mollon, 1997). Prior to the discovery of variation in peak sensitivity of pigments underlying normal color vision, it had been appreciated that female carriers of a red-green color vision deficiency have the potential for tetrachromatic color vision (Nagy, MacLeod, Heeyndermann & Eisner, 1981).
Here is a study specifically on color perception in heterozygous women that may answer further questions.
So there are some differences between color perception of heterozygous XX vs XY, they're just not colorblind per se.