Can dogs that are not in the working class still be used to work a herd? Chihuahua for example?

For example. I understand that a toy breed wont be as effective at cutting a cow from the herd as a blue heeler will, but could a chihuahua be trained to work? Would he do it? Would his size prevent him from being able to effectively intimidate cattle or sheep enough to move them or cut one out? What are your opinions on the feasibility of a chihuahua learning and performing herding. And if their size is too much of a factor with cattle, what about sheep or goats?