I dunno how fast a wood burning stove burns through wood, but I've got half of the back of a 3 car garage seasoning some poplars that died on my property. Maybe 7 of them? and they each took maybe an hour to fell, cut, and transport. I could see just meandering through the forest next to my property and ripping apart fallen trees with my electric chainsaw. Could easily clear a few truckloads without blinking.
I heat a 2700 sq ft space with about 3 tons of wood pellets every season (upstate ny) so i'd wager if someone was in a 1500 sq ft place, 2 tons or so of hardwood in a wood burner would likely do it unless the BTU's are much worse. Doesn't take much tree to clear that.
Biomass is one of the better heating methods as long as old growth isn't touched. Or if it is it's done very selectively and sustainably... most forests will repopulate gaps exceedingly quickly. Bonus points if you know how to target dead/dying trees, ones with girdled roots, rotting branch sockets, supported by dead trees, etc. Hell you can even collar them in-place and let them season themselves where they stand for a year or two.