In Elsa's case, her hair color is totally arbitrary. In the film sketches, Elsa is shown with black hair, and ice powers. The hair color relation to the ice powers seems to have been made as more of an animation design decision, and there does not seem to be any particular connection, link, or symbols between the two.

I think it has been confirmed that she would have brown hair like her mother.

^^ I did see a rumor on the internet that Elsa, Anna, and their mother could be mistaken visually as triplets, because aside from hair color, they all look the same. Lazy animation.

It's confirmed on twitter by one of the directors that she would be a brunette like her mom without the powers. I can't find it, but I have read it myself. I think you can find something about it on TVTropes' WMG page, I think that's where I originally read about it.

and it just makes logical sense anyway:

Ice powers touch/strike a person -> their hair turns platinum
Elsa has always been touched by her own ice magic -> her hair has always been platinum

I don't know. I've seen this idea before.

Considering Anna's hair changing and her parents hair colors, yes definitely

Her parents have dark hair.