Downplayed: Alice is a brunette who is very smart, but not in comparison to some other characters, who are redheads or blondes or gingers, who are super geniuses.
Alice finds her brown hair to be plain so she quietly goes about her business putting her effort into academics.
Or people with dark hair in the story are given some sort of Applied Phlebotinum that makes them intelligent.
If characters know that something needs to be done that's morally questionable and also physically challenging, they call on the brown-haired Dumb Muscle.
Or Alice is a Brainless Beauty who has chestnut hair. She doesn't mind when she doesn't understand her schoolwork because if she asks a male classmate with a smile and compliment to his intelligence, she can practically get him to do the work for her.
Subverted: Alice gets terrible grades, but is merely Book Dumb, just like a bunch of her peers.
...or Betty, after she dyes her hair, starts acting like a TV Genius when she clearly doesn't know what she's talking about and everyone except for Alice acts as if she's the smartest kid in class. Alice is not amused.
Zig Zagged: Alice is smart, but switches between blonde and brown hair so often that no one can be sure what is her actual hair colour.
Averted: Hair color has no correlation to intelligence.