The comment was a follow-on from Dachs's mention of 'classical Greek male statuary' above. Unfortunately the Greeks did not have public Forums, thus ruining the intended pun (displaying such images in a Forum, you see, is the subject of this thread), so a leap of faith from Greece to Rome was required.
Archaic statuary in Greece seems largely to have been limited to
kouroi and
korai, generally frontal male and female statues, usually exhibiting the so-called 'archaic smile'. The stereotypical
kouros was a completely naked male; the stereotypical
kore was a woman or girl in a
peplos, a kind of dress. These, however, were not, as far as we can tell, meant for public display. They are typically found in funerary contexts, in burial grounds and such.
Classical Athenian male statuary was focused on public figures (art for general consumption and later conspicuous consumption is usually said to be a product of the period of Alexander the Great and later) like generals and statesmen. The stereotypical general figure was completely butt naked, save for a helmet indicating what sort of person he was (i.e. a, uh, general) and sometimes an implement of war like a spear or shield. These, unlike
kouroi and
korai, were found in the most public places possible: on top of the akropolis, and in the agora below. Their entire purpose was for general display for the whole public. When public display of major figures extended to victorious athletes at the Delphic and Olympic games, these too were depicted in the nude.
Nude female statuary is historically supposed to have been an invention of the Hellenistic-period sculptor Praxiteles (4th c. BC) with his Knidian Aphrodite (although the type of the Praxitelean Aphrodite seems to have been one in which the vulva was covered by the goddess' hand, which can either be a gesture of modesty or titillation, depending on the view of the individual spectator). It seems as though most of these nudes went to the homes of private collectors, although a few were donated to temples and the Praxitelean Aphrodite herself was set up in an open-air temple, where at least one person seems to have attempted to copulate with her under cover of darkness. (We have the story from Pliny.)
Even after the inception of privately-funded and -purchased art in the Hellenistic period, art for public display did not cease to be produced, although it is less evident in the record compared to the explosion of private-sector statuary. This was true for both Greeks and Romans, although the Romans seem to have been slightly more wont to clothe their public figures (the Romans still loved buying nude statues as individual collectors, though!). Even then, one of the most famous - and grotesque - nude public statues was one commissioned of the Emperor Trebonianus Gallus (3rd c. AD). You can see it quite easily on Google Image Search by looking for 'nude Trebonianus': according to the statue, he was a massive, barrel-chested, somewhat pudgy dude wearing nothing but military boots, making the
ad locutio gesture, with a hilariously tiny head. A note on size: that statue is actually colossal, about 4/3 or 5/3 life size, IIRC. Gross! What we know of the nature of the statue's display seems to militate toward it being a public purchase by a Gallic (again, IIRC) town during the Emperor's rather depressingly short reign, presumably meant for display in the local
basilica.
tl;dr: yes, nude statues were definitely meant for public display and wide consumption in classical contexts.