Nelson’s album, Redheaded Stranger, is a concept album, I know (and therefore the “redheaded stranger” may not be even slightly autobiographical), but is (or was, at this point) the musician, indeed, a redhead?
Yes.
Here’s an album cover showing a young Willie: In The Jailhouse Now
A better example is “Hello Walls” which I was unable to find on the 'net.
It doesn’t look like it to me.
And in case you were wondering, that is the Willie Nelson.
He didn’t have Carrot-top flaming red hair, but it was red enough in his young days to be called red. My dad was the same way. His nickname was “Red,” but in his 30’s and later it looked brown with reddish highlights.