According to Jewish tradition, David was indeed a ginger - with pretty eyes, no less.
That’s not just Jewish tradition; that’s the Bible, 1 Samuel 16.
As usual, there’s a lot of leeway for translation here. The first bit of the description has, as I said earlier, been read as everything from red-haired to tan-skinned. But the rest of the sentence either says he has a handsome face with pleasing eyes, or a handsome face that’s pleasing to the eyes.
For example, here’s the YLT version: “And he sendeth, and bringeth him in, and he [is] ruddy, with beauty of eyes, and of good appearance; and Jehovah saith, `Rise, anoint him, for this [is] he.'”
On the other hand, the KJV says: “And he sent, and brought him in. Now he [was] ruddy, [and] withal of a beautiful countenance, and goodly to look to. And the LORD said, Arise, anoint him: for this [is] he.”
Various Bible commentaries (both Jewish and Christian) get into the meaning of this; see http://www.godrules.net/para/1sam/parallel1sam16-12.htm for some examples.