Grasslands are complex environments comprised of many different kinds of living organisms affected by abiotic factors such as weather. There are few things that are black and white in such complex ecosystems, but there may be some self-evident "truths." If you haven't considered them in your grazing operation, perhaps you should.
Grazing systems developed over the past 100 years attempt to optimize the productivity of pastures while at the same time produce a useable or saleable product. What most rotational grazing systems try to do is mimic the defoliation patterns under which grasslands were thought to have evolved; severe defoliation of native flora by massive herds of native ungulates (hoofed animals such as bison) for a relatively short period of time. Did short-term overgrazing occur by bison? Of course it did.
The integrity of these grasslands was maintained because bison would not return to these heavily grazed areas for many months or years, giving the land adequate opportunity to recuperate. Short duration grazing, high intensity-low frequency grazing, management-intensive grazing and, recently, mob-grazing have all been introduced as the grazing system that best mimics the movements of the great bison herds of the past. Fences were not in place back then, but rotational grazing occurred by herd movements over time. Isn't it interesting that these massive herds were able to maintain their numbers despite no one being around to feed them hay all winter long?
Diversity of grazing species
Historically, the Southern Great Plains was a very diverse ecosystem with a mixture of grasses, forbs, shrubs and trees on the landscape. Bison preferred herbaceous vegetation; woody plants were not their forage of choice. Fortunately, there were other ungulates that did utilize woody plants as well as forbs. Pronghorn antelope, elk, mule deer and white-tailed deer were common on the Southern Great Plains prior to European settlement. Today, domestic cattle have taken the place of the bison, and many cattle producers spend huge amounts of money trying to kill plants that some animals (e.g., deer, domestic sheep and goats) use. Fencing is a challenge for sheep and goats, but money spent on weed and brush control would buy a lot of woven wire fence. Cattle didn't pay for five-strand barbed wire fences the first year they were up, either.
The impact of fire on the Great Plains cannot be overstated. In addition to grazing, plant communities evolved with fire during all months of the year. The resulting regrowth was preferred by grazing animals, and Native Americans would use this technique to attract the great bison herds. Fire on the Great Plains has been reduced significantly since European settlement, resulting in increasing woody vegetation such as Eastern Red-cedar. Not using prescribed fire can lead to loss of grassland, landscape heterogeneity and plant diversity, not to mention the cost of trying to control woody plants with chemicals. Fire is not a stand-alone tool. In conjunction with a targeted grazing system and a diversity of grazing animals, you may be able to use forbs and woody plants instead of fighting them.