Animals chow down on vegetation using different methods, so it is important to make sure you have the right methods for your animals or the right animals for your fields.
If you have heavy overgrown vegetation, either for a field or in a lightly wooded area, cattle or buffalo would be a poor choice to let loose. These animals are grazers, content with keeping their heads down and chomping on grasses and then taking a half-step and eating that next lump of grass. They do not like weeds or other plants, although they will eat them if food is scarce. Horses are also grazers, but they're even more picky about what they eat. You wouldn't feed cow-quality bales of hay to your horses, and the horse bales come at a premium.
In this case, you want opportunistic grazers like goats. They'll chow down on bushes and weeds, then skippety-jump twenty meters to the next most succulent-looking plants they can see. They'll clear out underbrush fast. When that layer is gone, they'll go through again and eat the not-as-tasty stuff. Finally, they'll eat the lowly grass if that's all there is. One has to be careful because goats can clear a field down to bare dirt, which is bad for soil erosion.
Many farmers and ranchers will set goats into an overgrown pasture to get rid of weeds and brush, then migrate them to the next pasture and move the cattle and horses in to the vacated field. Lots of tasty grasses are available to the grass-eaters, plus now that the sunlight can get to the ground level it will help the grass to grow in nice and thick.
In many urban areas folks will rent out a herd of goats to clear out overgrown lots and properties without spraying toxic chemicals where kids (the human variety) may be playing. For pedantic folks who are interested, personally grazing your land will cause you to have stomach issues due to not having the enzymes, gut bacteria, and extra tummies needed to digest grass.