Well, the depiction of mythical characters changed over time; for instance, the heroes of the Iliad were portrayed with the Greek hoplite armour, even if Homer described a more archaic (and fictional, of course) kind of equipment.

So, Trojans and Phoenicians would have been imagined with an old-fashioned, exaggerated fancy style of clothing, resembling nevertheless the style of the time. As for Carthaginians, it's possible that they had seen many phoenicians who were subjects of the empire, and would likely have modeled mythical Carthaginians on them.

However, your reference to the "Caucasians" make me think you're referring also to physical features. But that couldn't be applyable in ancient times. True, there are references to the skin tone of the Aethiopi and Nubians, or to the blonde hair of the Galli and Germani; but there was no systematic distinction of "race".

Romans (who besides thought to be related to Anatolic Trojans) wouldn't have depicted a phoenician woman very differently from a Roman matrona

The skin tone, moreover, was used to denote gender rather than ethnicity; in the Greek world, since most women were confined at home, they were on average fairer-skinned than the males.

Interstingly, the stereotypical depiction of the Asian barbarian, as the Persians, was that of a fair skinned man, because it denoted softness and lack of manly valour.