Historically, hunting is often an activity associated with aristocracy. I think it's safe to say that hunting isn't as commonly mentioned in Roman literature as in other cultures, but it certainly does show up. A few emperors take some care to brand themselves as hunters, especially Domitian off the top of my head, who shows up a few times in stonework as a hunter. Suetonius mentions that he was fond of hunting.

In terms of literature, the best example I can think of is the scene from book IV of the Aeneid, where the grand nobility of both Aeneas and Dido is shown in a brief hunting scene before the two primary characters connect romantically. The pomp and circumstance of hunting with equipment and retinues is on full display, and Aeneas's son Ascanius in particular displays his budding manhood by fearlessly demanding more dangerous game to face off against. There's a whole vocabulary of spears, different types of nets, and slaves/assistants to hunt with that is clearly supposed to be familiar enough to the audience. Pliny the Younger mentions hunting as well in his letter 1.6, which amusingly is largely about how he is not an avid hunter -- he sits by the net, not with a spear, but with his stylus and tablets, and mentions that Minerva likes the wilderness as much as Diana does. While hunting isn't his thing, it's clearly A thing for the nobility, such that he's been swept up in going hunting with his companions even though he isn't interested in the hunt itself.

That raises an interesting question then -- what we do know about aristocratic hunting suggests that it was, to some degree, staged for the noble hunter. I have no doubt that a Roman nobleman might well be expected to have the skill to kill and butcher a deer, as he would very likely have done so for sport, but it might be strange for him to be expected to do the tracking itself, since mentions of Roman hunting for sport generally seem to involve descriptions of all the related paraphernalia.