I don't know anywhere that you can keep 1000 head of cattle without being subject to regulation by a government agriculture agency. All states have provisions for people to maintain large numbers of cats or dogs, in either a breeding or rescue/shelter facility, but they have to have a license to do it, and meet reasonable requirements aimed at maintaining the health and welfare of the animals.
I can keep 1000 head of cattle scattered across 12,000 acres of open range land in SD.