But it is more complex than that. We don't have deforestation issue from farming. Fields, even those that is just for hay are important for bio diversity and it is generally soils where other crops won't grow. We don't burn down old jungle forest to grow corn in order to feed cows that then get transported through half the globe. It is fields that if they get overgrown would remove the biotope that many species here depend on.
Highland cattle is the extreme end where they can basically live outside the whole year, and they do the job that people and motorized machines otherwise would need to do in order to maintain national reservations. I would be much interested in reading a study that compared the environmental effect of using forest machines vs letting cows keeping overgrowth down.