Cattle teach a new homestead a piece of law first. Arizona is a fence-out state, and this high-desert country is open range, which means the range cattle drifting across it with the water and the forage are entitled to be there. If they walk into an unfenced garden and eat it, that is not trespass in the eyes of the law. The burden runs backward from what a newcomer expects: on open range you do not fence the cattle off the land, the garden gets fenced away from the cattle.
The fence itself has a legal definition. A lawful fence in Arizona runs posts no more than 30 feet apart and carries at least four barbed wires, the top one 50 inches off the ground and the others at 18, 28, and 38 inches. Build that, and you gain standing: only inside a lawful fence can a landowner recover for what the cattle damage. Build less, and the law counts the loss as yours to absorb.
It cuts the other way, too, and harder than it sounds. Hit a cow on an open-range road and the rancher may owe you nothing for the wreck; you may even owe the rancher the value of the animal. The doctrine is old — Arizona courts confirmed the fence-out principle back in 1942 — and it is not blanket immunity: willful trespass and a few narrow no-fence districts change the math. But those districts sit on irrigated bottomland at the far edge of the county, not on ground like this. This parcel is open range, plainly, and the law starts from there.
As for the cattle themselves, do not trust the label. The desert herd is a mix, British breeds and their crosses, often with Brahman blood bred in for the heat, and only actually looking at the animals will tell you what is running this year. What matters to the homestead is not the breed. It is that they are a great deal of hungry animal with the legal right of way, and they will find any gap in the wire.
So the rule here is backward and simple: the cattle have the right of way, and the fence is the homestead's to build.