Edit: There is also archeological evidence for Romans with Sub Saharan ancestry reaching the UK. See e.g.
https://evoandproud.blogspot.com/2009/11/was-roman-britain-m...
Well, in Europe (and hopefully modern US) white includes the peoples not considered black (or asian etc).
Arabs for example are still white, Egyptians too, etc. Outside of racist circles were only WASPs or northern europeans were considered white (which was historically the case for most of the 20th century where white was hijacked for "northern European ancestry").
Egyptians for example, are also white. As are Arabs, middle eastern people, etc. But e.g. Ethiopians, or Ghana people are not (the majority of course, not that all citizens are not).
http://www.independent.co.uk/news/science/archaeology/ancien...
http://www.aljazeera.com/indepth/opinion/2015/07/arabs-white...
Generally I'd say that the whiter the population is, the higher the barrier to entry, so to speak, to being considered 'white'.
Of course it can have "brown skin". Egyptians, Tunisians, and co, including people in Souther Spain, Greece, Italy, Lebanon, the Middle East, and so, had, and still have brown skin, but are not black like e.g. Ethiopians (which ancients also describe), nor are depicted as such.