Some of the Grasshopper Sparrow nesting sites in the Willamette Valley (and even more so in the Umpqua Valley) are on grazing land with livestock, usually cattle. Examples include Ward Butte near Lebanon, along Goodrich Hwy north of Sutherland, and along Belts Rd. south of Brownsville. However none of those sites are regularly mowed for hay. Mowing is far more perilous for ground-nesting birds than livestock (which can be advantageous in other ways, in some circumstances in western Oregon).
Off-hand I can think of a couple of Willamette Valley sites in recent years where Grasshopper Sparrows were detected briefly, then disappeared after a field was mowed.