Heat oven to 375°F. Grease and flour two 4-cup and two 1-1/2-cup ovenproof bowls. In medium bowl, combine flour, cocoa, baking powder, baking soda, and salt. In measuring cup, combine milk and mint extract.
In large bowl, beat together sugar and butter on low speed until blended, about 1 minute. Increase speed to high and beat 2 minutes, or until light and creamy. Reduce speed to medium-low and add eggs, one at a time, beating well after each. Alternate flour mixture and milk mixture, beginning and ending with flour mixture; beat until batter is smooth, occasionally scraping sides of bowl with rubber spatula.
Divide batter among prepared bowls. Bake 30 minutes. Remove 1-1/2-cup bowls, and let cool. Continue baking 4-cup cakes until center comes out clean when inserted with a cake tester, about 10 minutes longer. Cool in bowls for 5 minutes. Invert cakes onto wire racks, and let cool completely.
In the top of a double broiler, over simmering (not boiling) water, beat together sugar, water, egg whites, light corn syrup, and cream of tartar on low speed until combined. Increase speed to high, and beat constantly for 10 to 12 minutes, or until stiff peaks form, scraping sides occasionally with rubber spatula. Makes about 4 cups.
Trim the flat side of each cake layer. Spread a thin layer of frosting on trimmed sides of cakes. Place same-size layers together to form two round shapes. Stand cake upright, and place smaller cake on top of larger one to form the snowman shape. Secure cake layers together by inserting a trimmed wooden skewer.
Spread a thin layer of frosting onto bottom of Ring Ding, and secure to cookie. Spoon remaining frosting into a piping bag fitted with a 1/2-inch star tip. Pipe a border around Ring Ding and place blue M&M's onto border to create a decorative hat. Place taffies together and shape into a scarf. Set the hat and scarf aside to firm up.
Transfer cake to a serving platter. Working down from the top, pipe star shapes around the entire cake. (If shapes are too pointy, gently tap down with fingertips.) For the face, arrange Junior Mints for the eyes, trimmed orange slice for the nose, and licorice string for the mouth. Wrap scarf around the neck. Place candy melts down middle of body for buttons; top with hat. Scatter rock candy around cake and serve.