Special equipment: 12 lollipop sticks; a 11-by-15-inch baking dish; a candy thermometer; 1-inch, 1 1/4-inch and 1 1/2-inch round cutters; a piping bag with a small tip
Dust an 11-by-15-inch baking dish liberally with confectioners' sugar. Pour 1/2 cup cool water into the bowl of an electric mixer fitted with the whisk attachment and sprinkle the gelatin over.
Meanwhile, combine the granulated sugar, corn syrup, salt and 1/2 cup water in a small saucepan. Bring to a boil over medium high heat and cook, swirling the pan occasionally without stirring, until the mixture reaches 240 degrees F on a candy thermometer, 6 to 7 minutes.
With the mixer on low speed, slowly pour the sugar syrup into the gelatin mixture. Once all of the syrup has been added, increase the speed to high and whisk until the mixture is bright white and forms very stiff peaks and the bowl has cooled and is just warm to the touch at the bottom, 8 to 10 minutes. Add the peppermint extract and mix to combine. Spread the mixture into the prepared pan, smooth the top and dust liberally with confectioners' sugar. Let sit overnight before cutting.
When ready to assemble, combine 1 cup confectioners' sugar and the cornstarch in a small sieve. Liberally dust a work surface with some of the mixture and unmold the marshmallow slab in one piece (you will need to guide it from the pan with an offset spatula and your fingers). Dust both sides of the slab well with the sugar-cornstarch mixture. Using 1-inch, 1 1/4-inch and 1 1/2-inch round cutters dipped in confectioners' sugar, cut 12 marshmallows of each size. Dust the marshmallows all over with the remaining sugar-cornstarch mixture.
Build the snowmen on the lollipop sticks, starting with the largest diameter marshmallows. Stick a licorice candy on top of each for a hat. With scissors, cut the gummy straws in half lengthwise. Flatten the pieces with a rolling pin to make flat scarves for the snowmen and tie them on. Stick the pretzel pieces into the middle marshmallows for "arms Use the orange candies to make noses.
Melt the semisweet chocolate in a small bowl in the microwave at 50 percent power in 15 second intervals, stirring after each, 45 seconds to 1 minute. Stir until completely smooth and transfer to a piping bag with a small plain tip. Pipe chocolate eyes, a mouth and buttons onto each snowman.
If making these on a particularly humid day, you can oil your cutters lightly to help cut the marshmallows. If they're too sticky, dust them with some extra confectioners sugar-cornstarch mixture.
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