Preheat oven to 350 degrees F. Line 3 sheet pans with parchment paper.
In large bowl, beat butter and sugars using electric mixer until light and creamy, about 3 minutes. Add egg and vanilla; mix until combined.
Add flour, baking soda, salt and cream of tartar; mix on low until incorporated.
Use a medium cookie scoop (#40, 1 1/2 tablespoons) to portion dough into 8 rounds for the bottom of the snowmen. Use a tablespoon to portion dough into 8 rounds for the middle of the snowmen. Use a teaspoon, portion dough into rounds for the heads of the snowmen.
Place each size of rounds on a separate prepared sheet pan. Bake cookies just until edges begin to turn golden brown, 11-13 minutes for large cookies, 7-8 minutes for medium cookies, and 5-7 minutes for small cookies.
Let cookies cool on the sheet pan about 5 minutes, then transfer to a wire rack to cool completely.