For the Cookies:
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.
For the Buttercream Frosting:
Beat butter, powdered sugar, vanilla and 2 tablespoons milk on high speed until smooth and creamy. Add more milk if needed to get a spreadable consistency.
Spoon frosting into a piping bag fitted with a medium plain round tip. Pipe frosting on top of large cookie, sprinkle with sanding sugar and place medium cookie on top. Pipe more frosting and sprinkle with sanding sugar, and place small cookie on top. Pipe top with frosting and sprinkle with sanding sugar.
Use the black gel decorating frosting to make the eyes and place a jelly bean for the nose. Use a bit of frosting to sandwich a mini chocolate cookie and peanut butter cup together to make a hat and place on top of the sugar cookie snowman.
Repeat to assemble remaining snowmen. For best results, serve the day they are assembled, but they can be stored in an airtight container at room temperature for several days.