For the cookies: Combine the granulated sugar, butter and orange zest in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium speed until smooth and fluffy, about 2 minutes. Add the vanilla and eggs and beat until fully combined, scraping down the sides of the bowl halfway through with a spatula.
Sift together the flour, baking powder and salt in a separate bowl.
With the mixer on low speed, add the dry ingredients to the butter mixture, alternating with the milk in 2 batches; mix until the dough comes together.
Divide the dough in half and flatten each portion into a disk. Place each disk into a separate resealable plastic bag. Refrigerate the dough until firm, about 2 hours.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper. Roll out both pieces of dough until about 1/4 inch thick.
Using 2 different sized butterfly cookie cutters (2-inch and 3-inch), cut out as many cookies as you can. Use the 2-inch cutter on one portion of dough and the 3-inch cutter on the other portion of dough. Be sure to dip the cutters in flour every other cookie or so while you are cutting them out to prevent the dough from sticking.
Transfer as many of the cookies as will fit onto the prepared baking sheets and bake until they're just set but not browned, about 7 minutes. Let cool 5 minutes on the baking sheets, then remove to racks to cool completely before decorating. Repeat with the remaining cookies.
For the icing: Combine the powdered sugar, milk and egg whites in the bowl of an electric mixer fitted with a paddle attachment and beat on medium-high speed until thick and glossy. Add more powdered sugar if the icing seems too thin. Add more milk if it is too thick. You may need to play with it until it is just right. The icing should be loose enough to stick to the cookies in an even layer, but not too loose to slide off.
For decorating: Divide the icing among 3 or 4 smaller bowls. Add 2 to 3 drops each of red and orange food coloring to each bowl, scattering it over the surface of the icing. Drag a toothpick through the drops a few times to make swirls.
Dip the top of each cookie in the icing and let the excess drip off over the bowl. Transfer the dipped cookies to a rack and allow to dry completely. When the colors in the first bowl of icing become too muddled, move on to the next bowl of icing and so forth until all the cookies are iced. Let the icing dry completely, about 1 hour.