In book 3 of his work Histories Herodotus refers to sheep which had big tails (3.113). So big in fact that the shepherds would make small carts which could carry the tails. Was it another Herodotus special? Well, probably not.
The fat-tailed sheep is a real species. These are located in Arabia, which is a comment Herodotus also made. The rationale behind their large tails is that this is where the fat is stored, something vital in desert conditions. Being on the tail also prevents the poor sheep from overheating.