They both mean the same thing but the second one sounds more natural. The first one works because hair colour behaves like a compound noun, and hair colours are specific things - blonde, red, mousy, etc, You could re-write them as: What is her hair colour? What colour is her hair? If we change this to something without specific colours, we see it only really works one way: What is the car colour? - This doesn't work but you could say: What is the car's colour? What colour is the car? - This is the natural way to ask.

Personally, I think it's more natural to say: What color is her hair?

What colour do they have(It is used for collective noun) like more than one What colour does she have( for singular) Both sentence are correct by the mean of of using right sentence at right time. . . I think so correct me if anyone could give better answer please.

There is no idiomatic use here. The grammar of the present simple tells us to put an s on the verb in the "he, she, it" forms. I have brown hair. She has blonde hair. When you make a "wh" question, you need the helping verb do. What color hair do I have? In the "he, she, it" forms, the helping verb takes the s. What colour hair does she have? She has blonde hair. Cheers

What color hair does she have is the idiomatic way of asking. Or you could say what color is her hair.