The over 125k miles of stonewalls were built in just thirty years because of sheep.
Hmm I had always thought that the deforestation was caused by demand for wood for heating and cooking.
Something about this sounds incomplete. A farmer isn't going to waste his time making a wall, especially the dodgy disorganized walls that are common in the region. A farmer doesn't need a shallow wall, stone or wood. The walls you come across in new england in the forest look exactly like people expect, a place on the edge of your farm to dump rocks. Now, maybe not frost grown, but New England has lots of rocks everywhere.
If you clear cut a forest it will be grass or brush or whatever in short order, a year or two. The roots of that vegetation, even just light grass is enough, will bind the soil all together as it freezes and keep the rocks from getting pushed up. You need a mostly dirt field to push up rocks. This means actively utilized pasture or farmland.
The walls were not dodgy and disorganized initially. Most of them were constructed before 1840 and have had close to 200yr of the ground moving under them to break them down. You occasionally see "good ones" on select areas of land where the soil and drainage situation made water in the earth basically nonexistent so therefore expansion and contraction were minimal and the wall aged gracefully. Damn near all of New England was clear cut pasture or farm at that time due to some circumstances in global commodities markets making it very worth everyone's while to raise sheep for wool on any land that they didn't need use some other way.
Nobody would have moved the rocks if they were not in the way, as would have been the case if they simply wanted the wood.
Animals have a habit of trying to get at the bottom layers of fence as they try and reach through for grass on the outside of the pasture and it's really hard on fencing over time. If you are rotating fields between pasture and crops or even just pasture it behooves you to drag the rocks away, straight to the edge is the shortest path. And if you're gonna do that it takes little extra effort to stack them well and create a rock wall for the lower portion of your fence. Spending that extra effort will pay you back in reduced wood fence maintenance.