1. Beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, vanilla, and 1/4 teaspoon salt; beat until combined. Beat in as much of the flour as you can with mixer. Stir in any remaining flour with a wooden spoon.
2. For each snowman you'll need to shape 3 balls of the dough -- one 1-inch ball, one 3/4-inch ball, and one 1/2-inch ball. Roll a portion of the dough between both hands -- this is a job that the kids can do. Use a ruler to measure the size of dough balls.
3. Place 3 balls for each snowman in decreasing sizes with the edges just touching on an ungreased cookie sheet. Press the balls together slightly but not enough that you change the shape of the balls. Leave about 1-1/2 inches between each snowman cookie. The 3 pieces for each snowman should be just touching.
4. Insert 2 miniature semisweet chocolate pieces in the smallest ball for the eyes, 1 chocolate piece in the middle ball for a button, and 2 chocolate pieces in the largest ball for two more buttons. Line up the buttons in the medium and large balls. Bake in a 325 degree F oven for 18 to 20 minutes or until bottoms of cookies are very lightly browned. Cool on cookie sheet for 1 minute. Transfer to wire racks and cool completely.
To make the icing, stir together 1 cup sifted powdered sugar and enough milk to make an icing that is the correct consistency for piping. Divide the icing into 3 small bowls. Tint one portion pink. This will be for the arms and the mouth. Tint another portion green. This portion is used for the broom. Tint the remaining portion orange; this will be used for the nose. Place each color in a small, heavy plastic bag. Snip off a corner of the bag to make a small opening.
The hats are made out of gumdrops. Sprinkle your work surface with a little granulated sugar. Flatten a large gumdrop to a thin oval shape that is about 1-1/2 x 1 inches, with a rolling pin. You also may need to add a little sugar to the surface of the gumdrop to keep it from sticking to the rolling pin. With your fingers, shape the oval into a cone and pinch the edges together. Roll up the bottom edge of the cone to form a hat brim.