sorry i thought you were asking about cleaning a small piece of carpet,
the best method for cleaning a sheep is strap it to the roof of your car and go through the car wash, surely.
Best method is similar to washing a sheep dog:
I - tie animal to a tree.
II - spray with a hose until thoroughly wet.
III - rub in large quantities of pet shampoo.
IV - hose off until water runs clear.
(Repeat III and IV if necessary)
V - untie animal and allow to dry naturally.
VI - groom when dry.
Also known as CWND = Cold water natural dry method.