Place the 100-percent wool sweater scraps in a washing machine (a top-loading machine is recommended). Fill the machine with hot water and regular detergent. Agitate the fabric on the longest cycle and rinse in cold water. Place the wool in the dryer for 30 minutes on regular heat.
Use a crafts knife to cut 1-1/2 inches off one end of a paper-towel tube. This will be the cupcake base. Cut a 1-3/4-inch piece of felted ribbing that is wide enough to wrap around the tube. Note: Use the finished edge of the ribbing for the bottom edge of the cupcake base.
Fold the ribbing in half crosswise with right sides facing; sew the ends together. Turn the ribbing right side out. Fold under a 1/4-inch hem around the top edge. Apply a band of glue around one end of the tube; press the inside folded edge of the ribbing into the glue; let dry. Apply a band of glue around the opposite end of the tube. Press the bottom of the ribbing into the glue; let dry.
Cut one 2 2-1/2-inch-diameter and one 3-3/4-inch-diameter circle from felted sweater scraps. Sew a row of gathering stitches around the perimeter of one circle. Pull the thread to gather the shape, leaving a small opening.
Stuff the opening with a pinch of fiberfill. Pull the ends of the gathering thread to close the opening and secure the thread. Repeat for the second circle.
Thread the cord through the jingle bell loop and knot. Stack the small frosting section on top of the large frosting section. Place the bell on top and secure by stitching through all layers of frosting and up through the bell loop.
Sew bead "sprinkles" onto the frosting sections.
Apply a band of glue around the top edge of the tube and folded ribbing. Press the frosting assembly into the glue. Use straight pins to hold the frosting assembly in place until the glue dries; remove the pins. Stuff the open end of the cupcake base with fiberfill. Cut a circle of sweater scrap for the bottom of the cupcake base. Apply a band of glue around the bottom edge of the tube and ribbing. Press the base onto the sweater circle; let dry. Trim around the perimeter of the cupcake base.
Wrap the cupcake base with rickrack or ribbon, tie the ribbon into a bow, and secure with glue.