Position a rack in the middle of the oven and preheat to 350 degrees F. Line a 12-cup standard muffin tin with cupcake liners.
Prepare the cake mix according to the package directions. Divide the batter evenly among the prepared muffin cups. Bake until done according to the directions.
Cool the cupcakes on a rack in the tin for 10 minutes, then remove them from the tin. Cool on the rack completely before decorating.
Meanwhile, combine the butter, sugar and salt in the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl if using a handheld electric mixer). Mix on low speed until mostly incorporated. Add the vanilla, increase the speed to medium-high and mix until smooth. Adjust the consistency with milk as desired. Fit a large pastry bag with a 1/3-inch diameter plain round tip or snip the tip of a large resealable plastic bag to make a 1/3-inch diameter hole, and fill the bag with icing. When the cupcakes are cool, hold the bag vertically with the tip pointing down at the center of each cupcake, and pipe a mound of icing onto each cupcake without lifting or moving the bag, so that the icing spreads to the edges, then finally lift the bag to form a mound on top.
Fit a small pastry bag with a small plain pastry tip, or use a small resealable plastic bag. Place the chocolate chips in a microwave-safe bowl; microwave, stirring every 20 seconds, until just melted. Transfer the chocolate to the prepared bag. If using the plastic bag, snip the very tip off so you can pipe the desired size. Pipe two dots for eyes on one flat side of each marshmallow, and a row of five dots for a smile. Pipe a little bit of frosting on top of the marshmallow head to glue the peppermint patty on top. Place a dot of chocolate on top of the patty hat to form a button. Place each decorated marshmallow "head" on the center of each mound of icing. Pipe 3 chocolate dots under the head to form buttons. Pipe two arms coming out of the snowman shoulders.
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