Preheat your oven and bake your sugar cookie dough according to your specific recipe or package directions, creating standard 2-inch round cookies.
Let the baked cookies cool completely to room temperature on a wire rack.
In a medium bowl, whisk together the powdered sugar, 2 tablespoons of milk, and the light corn syrup. Add another tablespoon of milk if the icing is too thick. You want a smooth, spreadable glaze.
Spoon a generous dollop of the white icing onto the center of each cooled cookie. Use the back of the spoon to gently push the icing toward the edges, letting it drip off naturally to look like a puddle.
Lightly coat a microwave-safe plate with non-stick spray. Place 3 to 4 large marshmallows on the plate and microwave for 3-5 seconds, just until they puff slightly and lose their perfect shape.
Quickly and carefully press one warm marshmallow onto the back edge of each wet, iced cookie. Repeat until all cookies have a marshmallow head.
Allow the cookies to sit undisturbed for about 30 minutes so the white icing can firm up.
Using the black decorating icing, pipe two small dots for eyes and a dotted smile onto the marshmallow head. Pipe two stick arms stretching across the white icing puddle.
Using the orange decorating icing, pipe a small triangle carrot nose onto the marshmallow.
Gently press two mini M&Ms into the white icing puddle to act as the snowman's buttons. Let the cookies dry completely before serving.