Step 1: Make animal appendages

Preheat the oven to whatever temperature your package of polymer clay suggests.  Make some little loops at the ends of the thin wires.

Make a rough shape for the legs, tail, and ears.  Carefully push the thin wire into the tail, inserting the straight end into the tip of the tail, gently pushing until it comes out of the end that will attach to the body.  Pull the tail along the wire until the loop is inside the tip of the tail and the long straight end is coming from the beginning of the tail that will attach to the body.  Smooth the clay over the exposed loop of wire, making sure it's fully enclosed.

Hold the wire while you add details.

I poked the sheep tail with a toothpick to make it look slightly fuzzy (or maybe just dimpled).

Carefully place the appendages on a sheet of foil and bake for about 15 minutes.

I premade all the legs, tails, and ears for the animals.  I also premade the sheep face, the pig snout, the rooster face, and the duck bill.  The cow tail has embroidery floss inside rather than wire, and the tip of the tail has exposed floss instead of clay so it will stay soft and fluffy.  Yes, the back legs on the cow are way too long for the front legs.  Please ignore my deformed cow.  :)