I laughed when I saw this question, and couldn't resist writing up an answer - albeit a brief and anecdotal one. As you might expect, Greco-Roman constructions of masculinity differed in many culturally-conditioned respects from their modern / western counterparts (the default ancient mode, for example, focused on martial virtue). There is, however, a family resemblance: classical men, like many men today, wanted to be seen as strong, powerful, attractive, socially dominant, etc. To that end, they adopted some familiar looking strategies...
They tried, for example, to look taller. The emperor Augustus - who was a little under 5' 7" - always wore platform shoes to make himself loom a bit more. (But since he was sensitive to the cold, his legs were perennially swaddled with bandages, which rather compromised the tough guy image.)
They dressed up like famously strong or brave men. One eccentric Greek general took this to the extreme of going into battle dressed - or rather, undressed - like Hercules: naked, with a lion skin wrapped around his shoulders and a club in hand. (Nero, we are told, once considered appearing in a similar state of heroic undress in the arena, and went so far as having a cooperative lion trained before deciding against it.)
They tried to incorporate the attributes of manly men into their daily routines. For most, this just meant some ostentatious weight-lifting and the like in the gymnasium or baths (Theophrastus has a humorous little sketch about a middle-aged man trying to exercise with youths). For the socially prominent, however, such play-acting might become a way of life. The emperor Commodus famously presented himself as a gladiator both in and beyond the Colosseum (he incorporated fatal archery into his dinner parties). Caracalla, likewise, sedulously imitated Alexander the Great, to the point of modeling his official portraits on the great conqueror's.
Speaking of art, we might turn to the whole idealizing classical tradition of representing even elderly and infirm men as athletes with bulging muscles. This was, of course, a complex mode of communicating certain things about social status, but it clearly partook of compensatory masculinity. For that matter, look at coin portraits - many Hellenistic kings and later Roman emperors liked to have themselves represented as bull-necked warriors to emphasize their military prowess and personal strength.
And yes, they tricked out their chariots - though gilding or otherwise pimping one's means of conveyance was more a matter of expressing wealth and status than masculinity per se. The best example I can think of is the mythical king Salmoneus, who - we are told - decided to imitate Zeus' thunder by dragging bronze kettles behind his chariot. (And in case you're wondering - yes, Zeus smote him for hubris.)
One might throw in the example of Gaius Marius; around 88 BCE, when his ally, the tribune Sulpicius, put his name forward to be given the command against Mithridates of Pontus, Marius tried to show his fitness for the job by exercising daily in the Field of Mars like young men did, despite being well past his prime and having put on a fair amount of weight. He had a clear, rational political reason for doing this, but it's hard not to see some personal issues involved in a guy in his sixties trying to prove his virility and strength like this, and secondary sources seem to commonly read it that way.
Marius, however, showing a spirit of keen emulation that might have characterized a youth, shook off old age and infirmity and went down daily into the Campus Martius, where he exercised himself with the young men and showed that he was still agile in arms and capable of feats of horsemanship, although his bulk was not well set up in his old age, but ran to corpulence and weight.
Plut. Mar. 34.3.