Instead of sheep, I have an angora lop rabbit. Rabbits make nice pets, but I obtained mine with an ulterior motive: angora yarn. So far, I have gathered a small Ziploc and a half of combings. It will take a long time to amass enough to spin.
But what if I added my cat's long hair and my dog's short hair? The cat is the color of toast, the dog mostly black, and the rabbit silvery gray. That would be an interesting yarn.
And before you scoff at the idea of spinning pet hair, you should read Knitting with Dog Hair by Kendall Crolius and Anne Montgomery.
Did you know Baryshnikov's leg warmers are supposedly made from his dogs' fur? And did you know that dog hair is warmer than wool? And once it is washed, it won't smell doggy?
This short book provides a primer on carding, spinning, and finishing pet yarn, as well as some patterns and resources and summaries of which breed produces what kind of fur.
I haven't actually tried making pet yarn, but it is an idea worth playing with. Besides, I have to groom my pets anyway; why not collect the fur and see what I can do with it?