The honest starting point: removing any vegetation carries risk
Plant roots hold soil together and slow water runoff; removing vegetation by any method — mowing, herbicide, hand-clearing, or grazing — temporarily reduces that protection until new growth returns. On a steep slope, especially ahead of a wet winter, that's a genuine consideration regardless of clearing method, and no method eliminates it entirely.
What differs by method is how the ground itself is affected while vegetation is being removed. Heavy equipment can compact or rut soil and, on steep or wet ground, machinery traffic itself can trigger slippage. Grazing animals distribute their weight across hooves rather than tracks or tires, and well-managed grazing leaves root systems and a stubble layer intact rather than stripping ground to bare soil.
What "well-managed" actually requires
The USDA's prescribed grazing standard and range science more broadly emphasize matching stocking density and timing to the site: overgrazing a slope — leaving animals on it too long or packing in too many for the terrain — can compact soil, break down root mass, and increase erosion risk just as much as any other method done carelessly. This is precisely why professional operations move herds through cells rather than leaving them on one hillside indefinitely.
For genuinely erosion-sensitive sites — steep grades, active landslide history, or proximity to waterways — best practice combines grazing with follow-up measures like straw wattles, seeding, or timing the work to avoid the start of the rainy season. Grazing is a fuel-reduction and vegetation-management tool, not an erosion-control certification on its own, and a responsible operator will say so rather than overselling it.