Preheat oven to 325F. Beat cream cheese, sugar, butter and vanilla with electric mixer on medium speed until well blended.
Add flour and baking soda; mix well.
Shape dough into equal number of 1/2-inch and 1-inch diameter balls. (You should have about 44 of each size ball.) Using 1 small and 1 large ball for each snowman, place balls, slightly overlapping, on ungreased baking sheet. Flatten to 1/4-inch thickness with bottom of glass dipped in additional flour. Repeat with remaining dough.
Bake 19 to 21 minutes or until lightly browned. Cool on wire rack.
Sprinkle each snowman with sifted powdered sugar, if desired.
