In a mixing bowl, beat butter with electric mixer 30 seconds. Add granulated sugar, water and vanilla; beat to combine. Beat in as much flour as you can. Stir in remaining flour and nuts.
Shape into 3/4- to 1-inch balls. (We used the smaller ball for the head.) Place on an ungreased cookie sheet. Bake in a 325° oven about 20 minutes or until bottoms are lightly browned. Cool on wire rack. Gently shake in a bag containing the powdered sugar.
Melt the candy coating and use to glue together three balls to form a snowman. Add pretzel sticks for arms.