Line a 9 x 13-inch baking pan with parchment, leaving overhangs on the two long sides.
In a medium bowl, whisk together the flour, cocoa, and salt. In a large bowl, using an electric mixer combine the butter, sugar, and food coloring until smooth and evenly colored. Add flour mixture, mixing only until just incorporated. Press dough into prepared pan and chill until firm, about 30 minutes.
Preheat oven to 325°F. Stab shortbread all over with a fork. Bake until the top looks and feels dry and sandy 35 to 40 minutes. Transfer to a wire rack to cool completely. Once cool, evenly trim the edges using a large serrated knife. Cut in half lengthwise then cut 1-inch rectangles. You should have twenty six 4 1/2 x 1-inch rectangles.
Microwave chocolate, in a small bowl in 30-second increments at 50% power, stirring in between, until melted and smooth. Spoon three rounds onto each shortbread rectangle, using the back of a teaspoon to spread into even circles. Immediately decorate with candies to make snowman and refrigerate until firm. Store at room temperature for 3 days or undecorated shortbread in the freezer up to 3 months.