I've often seen this done. The Hetch Hetchy pipeline operator uses it to clean up their right of way, which goes up, down, and through hills. Someone puts up a temporary electric fence around the right of way, and they truck in about a hundred goats. The goats graze everything down to bare dirt, and are then moved on to the next section.

I've seen this done with sheep, too. Those are easier to herd but not as agile on rough terrain.