Note: If using natural food coloring, be sure to shake the bottle before adding the coloring to the frosting.
To make the cookies:
Place an oven rack in the center of the oven. Preheat the oven to 350 degrees Fahrenheit. Line two baking sheets with parchment paper. Set aside.
In a medium bowl, combine the cookie dough and flour until smooth. On a lightly floured surface, roll out the dough to 1/4-inch thick.
Using animal-shaped cookie cutters, cut out shapes from the dough and place about two inches apart on the prepared baking sheets.
Form the scraps of dough into a ball, roll out to 1/4-inch thick, and continue to cut out animal-shapes. Bake for 10 to 12 minutes until the edges are lightly golden brown.
Cool for two minutes. Transfer to a wire rack to cool completely, which takes about 15 minutes.
To make the frosting:
In a stand mixer fitted with the paddle attachment, beat the butter until smooth, which takes about 20 seconds. Add the powdered sugar, vanilla extract and 1/4 cup water. Beat on low speed until combined. Increase the speed to high and beat until the mixture is smooth, adding more water, as needed, 1 teaspoon at a time until the frosting is spreadable.
Divide the frosting between three small bowls. Color the frosting by mixing in one drop of food coloring at a time until the desired color is reached. Spread the frosting over the cooled cookies and decorate.