I remember reading an analysis of how skin color in at least the television version of GoT was handled, and that analysis would disagree with you. I realize that at this point a link would be useful, but I don't remember where it was. However, I realize that is probably irrelevant to your point--GoT could be written as if being black means nothing, even if it doesn't happen to do that.
Ah, well, you've got me there. I have to admit I have not watched the TV series. I was just going by the books.
Tommy Pen, you mention the "race" of your character as "black." I speculate that you mean a dark skinned person? Like other posts have already mentioned, dark-skinned people are the world majority so I would suggest you give your character a nationality and say exactly where he's from. I retain little knowledge of history because I'm terrible with dates, but peoples from the continent of Africa have been all over the globe. For example, Moors were all over europe and ruled Rome, and dark-skinned people were in Asia and America long before they were "founded" by whites. So, even if your character is in Anglo-saxon land, they could be mixed with African heritage.