Make the body frame: Twist 2 pipe cleaners around each other in the middle, as shown. Fold each "leg" in half.
Wrap the body frame: working in sections, wrap white roving around the pipe-cleaner body and each leg.
Taper the roving near the ends of the legs.
Using the 36-gauge needle, needle-felt slightly as you work -- by punching at the fibers with the felting needle -- to secure. Use your fingers to pinch the ends of the pipe cleaners to make 4 "paws."
Punch the fibers all over with the needle until the body and legs are dense and firm.
With another piece of white roving, form a ball. Needle-felt the ball until it's firm. Attach it to the body by punching fibers of the "head" and "neck" with the needle, using a bit of additional roving if necessary; it may be easiest to do this against a felting-needle mat, which provides a firm surface for punching.
A large needle-felted piece sometimes ends up looking pocked. For a smoother surface, needle-felt a final thin layer of white roving over the head, neck, and body, loosely basting the wool to the body and letting it become slightly dense (so punch at it, but not for too long); it should look soft and fuzzy.
Cut 2 ear-shaped pieces from ivory felt. Attach to the sides of the head by punching them with the 38-gauge needle, folding in half to create ears.
Tear off 2 tiny bits of dark-gray roving. Using the 38-gauge needle, needle-felt them onto the head.
Make the Nose: Tear off 1 piece of light-gray roving. Using the 38-gauge needle, needle-felt onto the front of the head. (Alternatively, create the nose by punching a ball of the fibers on the mat, until they become slightly firm, and then attach to the head with the needle.)
White cotton pipe cleaners, 8 inches by 1/8 inch, blumchen.com
Merino wool roving, in Black, Pewter, and Pumpkin, and undyed merino roving, both by Ashland Bay, from the Yarn Tree
Felting needles, 36 gauge and 38 gauge, by Colonial Needle
Small felting needle mat (#8910), from Clover (optional)