I've been reading a book based on the siege of Carthage and at one point with in the book, there are some Romans in the City and they talk to the guard, and the guard says something along the lines of "you don't look like you're from around here, you look Roman". Is there any records of these people having very distinctive looks, such as Asians, Blacks and Caucasians have today?
The most obvious thing would have been that Romans were almost always clean-shaven (before the second century anyway), while Greeks and Carthaginians tended to wear beards. The different cultures would also have had their own distinctive hairstyles, sandal styles, jewelry, etc. A Roman trying to impersonate a Carthaginian could grow out his beard and dress in Carthaginian style clothing, but he could easily mess up the subtle details and look "off" to a local.
I realize that the ancient world did not have a modern conception of race, and so from a historians' point of view this question is irrelevant, but what would these peoples have looked like from a modern point of view? I know Italy was invaded multiple times by Germanic tribes, but were they big enough to impact the phenotypes of the population? What about Scandinavians before the Migration Era?
I know that a historian is not interested in these types of questions, but as a layman with a modern mindset, I'm curious as to how I would perceive and categorize members of these cultures, regardless of whether it is useful thing to do from an academic perspective.
Some research on how Romans looked is ongoing. The discovery that many of the marble busts were painted has offered some reconstructions. One can be found in this book (of Caligula):
The Color of Life: Polychromy in Sculpture from Antiquity to the Present edited by Roberta Panzanelli, Eike D. Schmidt, Kenneth D. S. Lapatin
The hair color and eye color chosen by the authors of that book were prior to the extraction of pigment and the use of a computer algorithm to reapply the pigment to a model marble statue (obviously not the original) in which Caligula looks like this:
More of this kind of work will give us hair color ranges for Romans. There are proprietary pieces of genetic software that allow reconstruction of hair color/eye color and more if the DNA is available. Naturally, that's expensive, but it might be a way of reconstructing what ordinary Romans looked like if their bones can be studied (always a difficult ethical prospect).
It's always hard to know if intermarriage among groups is taking place, as people have ideas about how such children should look (ideas that are not always accurate). Certainly, from ancient times until the present, Italy has had waves and waves of incoming DNA.
Diodorus, a Greek Historian, writes that the Celts( one of theses Germanic tribes) "are very tall in stature, with rippling muscles under clear white skin. Their hair is blonde, but not naturally so. They bleach it, to this day artificially washing it in like and combing it back from their foreheads. They look like wood demons, their hair thick and shaggy like a horses mane. Some of these are clean shaven, but others -- especially those of high rank, shave their cheeks but leave a moustache that covers the whole of the mouth and, when they eat and drink, acts like a sieve, trapping particles of food." Taken from "Salt" by Mark Kurlansky p. 54