Morrissey - Hairdresser on Fire
I embarrassed that I forgot about this one. Good find.
If we’re allowing “bald”, then Christine Lavin has a song about bald-headed men (she loves them).
1952 Vincent Black Lightning by Richard Thompson mentions “red hair and black leather, my favorite color schemes.”
“Hairshirt” by R.E.M. 
“Pencil Thin Mustache” by Jimmy Buffett
“Come Together” by the Beatles (He’s got hair down to his knees)
I came in to mention this one. It was the best song on “Born This Way” but for some reason never released as a single.
No, no. That was “I dream of Jeannie. She’s a light brown hare.” 
I knew you knew that.
**Red-Headed Woman **- Bruce Springsteen
Well I don’t care how many girls you’ve dated, man
You ain’t lived till you’ve had your tires rotated
By a red headed woman
(and it gets raunchier)
[quote=“Accidental_Martyr, post:63, topic:696159”]
“Hairshirt” by R.E.M. 
Can’t believe you didn’t list Werewolves! Not entirely about hair, but it sounds like he had a great head of hair on him. NNTT!!!
“What Is Truth?” by Johnny Cash
A young man is sitting on the witness stand.
The man with the book says “Raise your hand.
Repeat after me, I solemnly swear…”
Then the man looked down at his long hair
And although the young man solemnly swore,
Nobody seems to hear anymore.
And it didn’t really matter if the truth was there-
It was the cut of his clothes and the length of his hair.
And the lonely voice of youth cries
“What is truth?”
“Signs” by the Five Man Electric Band
And the sign said,** LONG-HAIRED FREAKY PEOPLE NEED NOT APPLY**.
So, I tucked my hair up under my hat and I went in to ask him why
He said, “You look like a fine upstanding young man. I think you’ll do”
So, I took off my hat and said, “Imagine that! Me working for you!”
“I saw a werewolf drinking a pina colada at Trader Vic’s, and his hair was perfect”.
That’s true, his hair was perfect. 
Branching out a bit…
“Nature Girl” by Downright.
“Map of Tasmania” by Amanda Palmer. (NSFW)
He isn’t any more, really. He just came and left*
Ringo Starr (with the Beatles): Don’t Pass Me By
I’m sorry that I doubted you
That was so unfair
You were in a car crash
and you lost your hair
–G!
- a residue…:o
I’m a big Richard Thompson fan and I love that song!
For some more Canadian content: I’ve Seen Pubic Hair
If any of you were in the Cavalry, you’d have thought of"(For In Her Hair) She Wore A Yellow Ribbon".
And in one of the Reverend Richard Penniman’s most famous hymns, John is healed of his misery by a bald headed nurse named Sally, seemingly against John’s wife, Mary’s, wishes. Obviously , the hymn is a statement FOR modern medicine and against faith healing.
If “songs about hair color” answer the OP’s question, how could we possibly leave out 'Cause I’m a Blonde by the incomparable Julie Brown?
From the other side of the classical divide:
Strauss has a lovely song, “Breit’ über mein Haupt dein schwarzes Haar,” that basically says, spread your black hair over me so that all I can see is the night of your hair and the stars of your eyes.
Sweet Child of Mine Guns and roses
Her hair reminds me of a warm safe place
Where as a child I’d hide
And pray for the thunder and the rain
To quietly pass me by
Nick Cave, singing about P J Harvey’s Black Hair. And Ron Sexsmith sang Strawberry Blonde.