You (or rather, your kids, right?) will have fun dancing these little piggies across the kitchen and all over the house — just hope that they don't leave a trail of crumbs behind to clean up. Of course, piggies are messy little animals, and so are the people that eat them.
In a bowl, whisk together the powdered sugar, milk, and vanilla extract. Divide the icing into 2 parts, with most of it going into a medium-sized bowl. Use food coloring to tint the larger batch of icing. Leave the remaining frosting untinted.
Line baking sheets with parchment paper or silicone mats, or grease generously with cooking spray. Using a mixer fitted with the paddle attachment, beat the butter and sugar in a large bowl on medium-high speed until fluffy. Add the vanilla extract and beat until combined.
In a separate bowl, stir together the flour and baking powder. Add the flour mixture slowly to the butter mixture, beating on low speed. Stop beating as soon as the flour is incorporated (overbeating will produce a tough cookie). Form the dough into a ball, cover in plastic wrap and refrigerate for 30 minutes before rolling it out.
Meanwhile, preheat the oven to 350 degrees.
Lightly flour a flat, smooth surface. Roll out the chilled dough to ¼-inch thickness. Cut the cookies with a 4-inch pig cookie cutter. Use a spatula to transfer the cookies to the baking sheets, placing them ½ inch apart. Combine the dough scraps and reroll the dough to cut more cookies.
Bake the cookies until light brown around the edges, for 10-12 minutes. Cool the cookies for 10 minutes on the baking sheet. Remove with a spatula and cool completely on racks about 5 minutes before icing.
When the cookies are cool, dip them face down in the pink icing, being sure to cover the whole cookie. Set the cookies, icing side up on parchment paper and let the icing harden before continuing to decorate.