From Muppet Wiki

Shirley and Nat Muskrat are a married couple who appeared in Emmet Otter's Jug-Band Christmas. The two muskrats performed a dance act as "Carrots the Dancing Horse" at the Waterville talent show. Shirley was the front-half and Nat was the back - however, they had a hard time keeping it together (literally).

Unfortunately, Shirley and Nat's act did not impress the judges and they lost the competition to Riverbottom Nightmare Band.