I can't for sure say if the moors where black or white or whatever from traditional historical connection but from a theatre history perspective a lot of times moors or moor characters where portrayed as black skinned and this goes all the way into the time of Shakespeare(hell even after).
In Europe, they have the border morris(moors?) in which they put on blackface dance in groups.
However, In many of these plays they do not portray the "moors" in a positive light.
The types characters run amok from slaves, lovable sidekicks, treacherous bandits to cunning conmen.
“In medieval Spain, Moors and Jews became the primary symbols of the “low other” in festival performances. Medieval writers often characterized Moors as treacherous and cowardly in moros y cristianos plays. ”
Excerpt From: Phillip B. Zarrilli, Bruce McConachie, Gary Jay Williams, and Carol Fisher Sorgenfrei. “Theatre Histories.”
I'd say there were also berbers and arabs as Arab was the language of the Moors unless I'm deeply mistaken and I need to up my research game 
