Open packages of dough; separate into 4 equal portions. Tint 1 portion red, 1 portion yellow, 1 portion orange (mixing red and yellow) and 1 portion turquoise (mixing blue and green).
Divide each colored portion of dough into thirds. Measure burro-shaped cookie cutter (or desired shape) and find a container as deep as the cookie cutter is tall.* In container, alternately layer colors of dough in desired order. Cover; refrigerate until firm.
Heat oven to 350°F. Line cookie sheets with cooking parchment paper. Remove dough from container; cut into 1/4-inch slices. On cookie sheets, place slices 2 inches apart.
Bake 6 to 10 minutes or until set. While still warm, cut cookies with burro-shaped cookie cutter. In 16 of the cookies, use small round cookie cutter to cut out center of burro. Gently remove cutout portion of cookie. Cool 5 minutes; remove from cookie sheets to cooling racks. Cool completely.
In small bowl, mix powdered sugar, milk, corn syrup and vanilla with whisk until smooth. Tint with desired food color. Spoon icing into decorating bag fitted with small round tip or small resealable food-storage plastic bag with tiny corner cut off.
For each sandwich cookie, pipe icing around top edge of 1 whole burro cookie. Top with 1 burro cookie with cutout center; pipe icing around edge of burro. Fill hole in center with candies. Top with second whole burro cookie.