Start with two store-bought 2 1/4-inch pom-poms and one 1 3/4-inch pom-pom. Trim one large pom-pom to be slightly smaller. Cut 3 pieces of gray yarn (for buttons) and 2 of black yarn (for eyes), each 5 1/4 inches long; knot each in center. Thread ends of each yarn piece through pom-poms (use a yarn needle, and work with one end at a time) where shown, tying yarn in back. Glue on orange felt carrot nose. For hat, cut 3/4- and 1 1/4-inch circles and 2 1/4-by-3/4-inch rectangle of red felt. Sew a red yarn loop to small circle. Glue rectangle into cylinder and to edge of small circle; glue to large circle.
Sew up from the bottoms with needle and invisible thread, sewing through centers of pom-poms to join them and sewing through bottom of hat; then sew back down through centers, and knot. Tie on ribbon scarf.