I propose a Frame Challenge
In reality, herd animals are frequently found in meadows and large open areas despite eons of hunting, which, presumably, would lead to the animals that survive being those that were more likely to stick to the trees.
The problem is that herd animals need a ton of grazing space — which is very difficult to find in forests.
Add to this that you have areas like the African Savannah that's chuck full of tasty treats with very few trees about.
William of Ockham, an English Franciscan friar (1287–1347), is credited with formulating the Law of Parsimony that we know better today as Occam's Razor, which can be simplistically stated: "All things being equal, the simplest answer is usually correct."
The simplest answer is that your dragons would populate in areas with large open spaces where herd animals dwell rather than seek the more fantasy genre driven habitat of forested mountains. This is especially true as dragons, like most herpetological critters, will be fond of warm areas. That means closer-to-the-equator latitudes, lower elevations, and open/rocky areas for habitation. If they must have caves, they'll be volcanic (warmed by the earth, not the sun).
You don't have a problem because no dragon in its right mind would try to hunt in a forest. Unless they have human or near-human intelligence, the idea that burning down the forest before chasing an animal into the area simply wouldn't happen. The burning part would be as a consequence of chasing something into the forest — but that's not going to burn down the world's forests. In fact, once the prey is in the forest, despite having ignited it, the hungry dragon would turn around and chase down something easier to see.
They'd favor large open spaces and avoid forests completely. It's how they'd evolve.
And this assumes they use fire-breathing as a means of obtaining a meal. Fire is destructive, so unless they live on ash (see the movie "Reign of Fire," which brilliantly used this as a way of justifying why dragons burn everything they see), the use of fire would be defensive, not offensive. Like eagles and other raptors, they'd want large open spaces to swoop in, snag breakfast, and haul it back to the kiddies.
@User3445853 brought to my attention Australia's Firehawk Raptor, a remarkable bird that will pick up burning brands in their claws and beaks to intentionally set fires, forcing their prey to bunch up and run in one direction. This certainly weakens my frame challenge — but I'm going to stand by it anyway because I don't think it's without merit. But that was some great insight!