You can describe a person's hairstyle with this phrase:
She wears her hair long.
He wears his hair parted on the left side.
People use this expression for talking about someone's hair length, the way that they style it, the direction that it's pointing in, and so on. They don't usually talk about hair color this way, even if a person dyes their hair.
You can also just describe hair like this:
His hair is slicked back.
She has long hair.
The phrase "wear (one's) hair ___" is used more for describing people who the listener doesn't know.