Would a system of caste system based on hair color work for a medieval society? The lighter the color the higher you would be. This question assumes that the people of this worlds hair color is hereditary and the people living here have not discovered hair dye. How stable would this caste system be? Is there any blatant problems with this system?
It would be a very rigid cast system since it would be hard to impossible to change your lot in life. and what about bald people? or the aged? White haired old men and women? Do they get raised by virtue of age and wisdom? What about those who are bald? Where do they fit in? Is a shaved head a mark of shame, having their locks shorn from their head? Would wigs or some other mark be given to the few who are elevated above their station?
Well, the exact scenario presented in your question seems unlikely to me. For one thing, unless your world is illogical, you need to come up with an explanation for why hair dye, wigs, and other ways to change hair color continue not to be invented. For another, if people mate in non-random ways, other minor genetic differences will probably develop between castes that will cause other differences in appearance (In fact, it seems likely that the castes have been somewhat different in ethnic makeup since the beginning). Lighter hair might be one feature associated with higher castes, but it seems unlikely to be the only one.
In fact though, it seems to me that hair color could be part of a caste system even if hair dyes exist. All you need is sumptuary laws for hair, that forbid low-class people from dyeing their hair or wearing light-colored wigs but that allow this for members of higher castes.
Anyway, a relevant real-life example might possibly be Brazil, where class and skin color have some connection. Obviously, there is not a caste system.