Heat oven to 350°F. Cut cookie dough in half lengthwise to make 2 long pieces; refrigerate one half until ready to use. On floured surface, roll half of dough into 8x5 1/2-inch rectangle (use edge of ruler to make sides straight).
With sharp knife, cut dough rectangle crosswise into 4 (5 1/2x2-inch) rectangles (see diagram). Cut each small rectangle diagonally into 2 triangles; place triangles 2 inches apart on ungreased large cookie sheet. Bend tops of triangles as desired to resemble stocking caps.
Bake 7 to 11 minutes or until edges are light golden brown. Cool 1 minute; remove from cookie sheet. Cool completely, about 15 minutes. Repeat with remaining half of dough.
Divide frosting into 3 small bowls. Leaving 1 portion white, stir red and green food color into remaining portions. Frost each cookie with about 1 tablespoon red or green frosting. Frost about 1 inch of short side of each triangle with about 1 1/2 teaspoons white frosting for hat brim. Sprinkle brims with coconut. Place marshmallows on ends of hats for tassels. Let stand until set before storing.