What determines hair color and skin color?

They are both polygenetic traits, meaning more than one gene is associated with each. For that reason they do not necessarily follow the classic Mendellian pattern of predictible outcomes.

@pdworkin is right. The distribution of polygenic traits (think height) usually come out to look like a bell curve, which is why both of these traits look like continuums rather than something where you can affix “dominant” or “recessive” to a particular color.