Combine all ingredients in the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl if using a hand mixer). Mix on low, scraping the bowl occasionally, until the mixture forms a cookie dough. Be sure to start on low or the dry ingredients will fly everywhere!
Divide the dough in half. Place a large sheet of waxed paper on a large cutting board or flat surface. Place the cookie dough on the wax paper. Place another large sheet of wax paper on top of the cookie dough. Press down into a flat disk with the palm of your hand, then roll out the dough between the two pieces of wax paper. After each 3-4 rolls, carefully lift the top sheet of wax paper off the dough, then replace it, flip the dough over, and carefully peel the other wax paper sheet, replace it, then continue rolling until the dough is about 1/4” thick. Place the dough, still between the wax paper sheets, on another cutting board or cookie sheet.
Repeat with second half of dough. Place both rolled out cookie dough sheets in the refrigerator for at least 30 minutes (or wrap them well with plastic wrap and chill overnight).
When ready to cut cookies, preheat oven to 375°F.
Cut cookies in snowman shapes and place them on a parchment or silpat lined baking sheet. Chill cookies on sheets for an additional 10 minutes or so, or until they’re hard to the touch.Bake cookies for 6-10 minutes depending on the size. I take them out as soon as the bottoms start to brown because we like them softer. If you want crunchy cookies, let them cook longer. Cool completely before frosting and decorating.
To make frosting, beat butter until smooth in a large bowl with an electric mixer.
Slowly mix in powdered sugar, then vanilla and 1 tablespoon of milk at a time until the frosting is the consistency you desire.
To decorate them as I did: Frost with white frosting. Tint some frosting black, red, orange, and green. Use a Wilton #3 or #4 tip to frost the scarf, hat, buttons, eyes, and carrot nose. If you want to do the “furry” snowman with sprinkles, frost the cookie with white frosting and dip the cookie upside down on a plate covered with white sprinkles, sanding sugar, or nonpareils. You can also use sprinkles to make the eyes, nose, mouth, and buttons.