Cattle can definitely be 'dog broke.' It just takes awhile, as you mentioned and it takes a dog with a lot of confidence and perserverance, or the cows win. We just never had to take our dogs where cattle weren't used to dogs. Having them in those kind of cattle for one day would be really hard on the dog.
Trey Gowdy, "One person does not make a law in a Republic. The president cannot make laws by himself."