Well, he was a young man, since he died in his early 30's (33-34 I believe). But the Bible never mentions his racial makeup. He was Jewish, so that would usually indicate he was fair skinned, but as I have mentioned (and most Christians believe) it doesn't even matter. And he's depicted as having a beard and long hair mainly because in those days and that area many men had beards and longer hair. Jesus did preach about long hair being the lifeblood of women so him having long hair, I believe, is wrong. I think he had shorter hair and a beard. But again, his appearance doesn't really matter.
And when you go out of your way to say Jesus would have been brown or black, that's bringing race into something that has no business being brought into. He died for all of us, not just white folk.