Welcome to SlowTrav Bette; I know the area around Orvieto 'bout as well as any, having walked most of it. If then it matters to you what type of countryside you're in, do specify; N, S, E, and W of Orvieto the landscape (and roads) vary enough to make the query useful, from rolling farmland to trafficky and dangerous highway, to kinda wild.

OK, cows it is. Now (a) with a car, distances are small; (b) there's going to be cattle everywhere, sort of, even if as you say, not like Texas. That said, you can maximize your cow quotient by — unfortunately — hugging the E35 Rome-Florence superhighway. Unfortunately, because the road is a blot; maximize, not because kine love highways, of course, but because the highway follows the Tiber and the flat more crop-growing and grazing country.

North of Orvieto within your distance, and a bit off that highway, anything along the smaller road (the SS 7, parallel to and just two or three miles, most of the time, to the east of E35) would be peaceful, occasionally good views, certainly agricultural; i.e., not forested hilly unkind-to-cows areas like the road from Orvieto to Todi.

In particular, I'd try to focus on the patch between Sala at the S end and Città della Pieve at the N end. Ficulle, pretty much at the S end of that stretch, is firmly agricultural, although its main crop is "Orvieto" wine (most of which is grown not near Orvieto but up toward Ficulle, in fact). Still, Ficulle (see its little section of my site) is a good place, with at least one good Gothic church, too.

Central Italy, (in my speak, that's often a code word for Umbria, the part of it I know best) may not be Cattle Country, running instead to sheep and pigs, but what cattle it has, it's particularly proud of, and you might be interested in tracking down a breeder: the breed in question is the Chianina (pron.: kyaNEEna), a broad-shouldered white cow originally bred as draft animals, but now with tractors, they've discovered that the meat is better than that of many others. There are stories afoot that it is descended from the special breed of white cattle used as sacrificial animals by the Romans; and although it's possible, and the modern Chianina (see my photo) does look like the cows shown on say the Ara Pacis in Rome, it seems unlikely to me because of the intervening dark ages; I think it would have been very hard to keep good breeding strains going thru the 600 years of barbarian, Lombard, Arab and Norman invasions. Anyway, if you're interested, see the rest of my footnote on the page with the photo to get you started.