Good question.

Actually although Romans did portray nudity in their art (due in large part to Greek influences) they were far from OK with public nudity. Ennis stated that "exposing naked bodies among citizens is the beginning of public disgrace." That's pretty clear on Roman attitudes there, and even when exercising Romans wore loincloths or skirts unlike their Greek counterparts.

Plus POWs and slaves were often stripped naked, so it had that unfortunate connotation, as well as modesty being a symbol of dignity, citizenship, self-control and masculinity in men. Interestingly enough, Romans seem to have been more comfortable with partial female nudity in art than their Greek counterparts, but again, definitely not when it comes to actual citizens doing it in public.

Excepting the baths (and even here for much of Rome's history it was complex and changing in how open it was to various ages, and just males for a long time, for modesty's sake) public nudity was frowned on.

But speaking of Marcus's Antonius's unconcealment, Cicero is pretty harsh in his letters about him appearing half-naked at Lupercalia (even though it was a fertility festival and as one of Luperci, or Brothers of the Wolf, Marc Antony was required to.) That said, Cicero hated Marcus Antonius in general. Augustus reformed Lupercalia and other festivals like Rosalia by toning down the nudity, and generally making them a bit tamer.

This is a good example of both the "Romans = Greeks" and the equally prevalent "Pagan = amoral" idea many writers employ.

Letters of Marcus Tullius Cicero

Livy

Pliny's Natural Histories

Ennius

Ovid's Fasti