Preheat oven to 400 degrees F (200 degrees C). Grease cookie sheets.
Beat in the eggs one at a time, then stir in the vanilla.
In a mixing bowl, mix the butter, sugars, egg mixture, cinnamon with a wooden spoon until creamy and fluffy. Sift flour in it until blended and smooth and wrap dough and refrigerate for 30 minutes.
Roll dough out on a lightly floured surface until 1/4 inch thick. Cut out cookies using a 2-inch round cutter and place 2 inches apart on ungreased baking sheets. Gather and reroll dough scraps.
Bake for 15 minutes until golden not browned. Let stand on baking sheet for 2 minutes. Remove from cookie sheets to cool on wire racks about 10 minutes.
Put the icing sugar into a bowl and add cold water a teaspoon at a time until the mixture is runny but thick enough to coat a spoon. Snip the marshmallows in half using wetted scissors.
Spoon a little icing onto each cookie and attach half a marshmallow. Using a little icing, stick the other half on top at an angle. Drizzle a little more icing onto the cookie to make melting snow.
Break the pretzel sticks in half and place on the cookie for arms. Stick orange chocolate beans on for the noses. Stick three chocolate beans on each cookie to represent buttons.