Preheat your oven to 350 degrees Fahrenheit. Line two large baking sheets with parchment paper or silicone baking mats to ensure the cookies do not stick and are easy to remove after baking.
In a large mixing bowl, beat the softened butter and granulated sugar together until the mixture is light and fluffy. This usually takes about two to three minutes with an electric mixer.
Add the egg and the alcohol-free vanilla extract to the butter mixture. Beat again until everything is well combined and smooth, scraping down the sides of the bowl as needed.
In a separate small bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until a soft dough forms. Do not overmix, as this can make the cookies tough.
Roll the dough into one-inch balls and place them two inches apart on the prepared baking sheets. Bake for 8 to 10 minutes, or until the edges are just barely golden. Remove from the oven and let them cool completely on a wire rack before decorating.
Whisk together the powdered sugar and milk in a small bowl until you have a thick but spreadable icing. Spoon a small amount onto each cooled cookie, spreading it toward the edges in an uneven circle to look like a melting puddle of snow.
While the icing is still wet, place a marshmallow near the back or side of the “puddle” to act as the head. Let the icing set for a few minutes so the marshmallow stays in place.
Using the orange icing, draw a small carrot nose on each marshmallow. Use the black icing to dot on eyes and a coal mouth, then draw stick arms onto the white icing puddle. Add small candies or dots of icing for buttons to finish the look.
