In the bowl of a stand mixer fitted with the whisk attachment, combine water, yeast, and honey and whisk to dissolve yeast. Let sit for 5 minutes.
Switch to the paddle attachment, then add sugar and eggs and mix to combine. Add flour, salt, and mint extract and mix on low until the wet and dry ingredients come together. With the mixer running, add the butter in 3 additions. Increase speed to medium-low and mix until the dough blends together, about 2 minutes.
Switch to the dough hook attachment and knead the dough on medium-low speed until it forms an elastic ball and pulls away from the sides of the bowl completely, about 5 minutes. Transfer dough to a large greased bowl, cover with plastic wrap, and refrigerate at least 4 hours and up to overnight.
Punch down the dough and turn it out onto a lightly floured work surface. Roll the dough out to a generous ¼” thickness. Cut into rounds with a 1” cutter and transfer the donut holes to a lightly floured parchment-lined baking sheet. Let rise 20-30 minutes; the donut holes will feel light to the touch but not deflate when they are ready.
Meanwhile, heat about 4” of oil in a large, heavy-bottomed pot to 330 degrees. Fry donut holes in small batches until evenly golden brown, constantly moving and rolling the donuts, about 1 minute. Transfer to paper towel-lined baking sheet to drain.
Generously dust donut holes with confectioners sugar, tossing gently to coat completely. Use aluminum foil to create three balls of varying sizes to form the body of the snowman and transfer to a cake stand. Affix donut holes to body using toothpicks, then decorate snowman as desired.
TO MAKE THE SAUCE:
In a small saucepan, combine cream, candy canes, and salt. Bring to a simmer, whisking to dissolve the candy canes completely. Pour the liquid over the chocolate chips in a medium bowl and whisk until smooth. Serve warm.