Cream butter and sugar until fluffy and pale, about 5 minutes. Beat in vanilla and egg.
Sift in flour, baking powder and salt, mixing until a soft dough forms.
Divide dough into two equal parts. Flatten each portion into a disk and wrap well in plastic wrap. Chill for about 45 minutes.
Preheat your oven to 170°C conventional. Line two baking trays with baking paper.
Remove one disk and unwrap. On a lightly floured work surface, roll the dough out to about 5mm thick. Cut out as many circles as you can using a 7cm round cutter. Place rounds on the prepared baking trays, spacing them 3cm apart. Repeat with the rest of the dough.
Bake for 12-14 minutes, or until edges are golden brown. Transfer baking trays to a wire rack to cool. To make the white icing, stir together icing sugar and milk until smooth. Add up to 1 teaspoon more milk as needed to get a thick spreading consistency. Spread icing over cooled cookies and press a marshmallow at the top of each cookie.
To start decorating your cookies, cut down the spine of the snake lolly to produce two long thinner pieces. Wrap each piece around the base of the marshmallows to form scarves.
Using an orange snake lolly, cut small triangles to form the Snowman’s nose. Dip in the icing sugar mixture and fix the nose to the middle of the marshmallow.
Place three mini round coloured chocolate candies down the centre of the cookie to form buttons. Using the black food pen, style your snowman’s face, and draw two arms.