Description from the book:

"The salty Dornishmen were lithe and dark, with smooth olive skin and long black hair streaming in the wind. The sandy Dornishmen were even darker, their faces burned brown by the hot Dornish sun. They wound long bright scarfs around their helms to ward off sunstroke. The stony Dornishmen were biggest and fairest, sons of the Andals and the First Men, brown-haired or blond, with faces that freckled or burned in the sun instead of browning. [A Storm of Swords, p. 520]"

"The princeling removed his helm. Beneath, his face was lined and saturine, with thin arched brows above large eyes as black and shiny as pools of coal oil. Only a few streaks of silver marred the lustrous black hair that receded brown his brow in a widow’s peak as sharply pointed as his noise. A salty Dornishmen for certain. [A Storm of Swords, p. 521]"

The general idea is that they are somewhere between Spanish and Moroccan in appearance: swarthy and dark, but not 'black' as such.