In a large mixing bowl beat shortening and butter or margarine with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, baking powder, and salt. Beat until combined. Beat in egg, 1 tablespoon milk, and 1 teaspoon vanilla. Beat in as much of the flour as you can with the mixer. Stir in remaining flour with a wooden spoon. Divide dough in half. Cover and refrigerate about 3 hours or until chilled dough is easy to handle.
Roll half of the dough at a time 1/8 inch thick on a lightly floured surface. Cut dough into diamond shapes (2-1/2 to 3-1/2 inches across); bend the top point of each diamond to the side to make Santa's hat. (Or, use Santa cookie cutters.) Place 1 inch apart on ungreased cookie sheets.
Bake in a 375 degree F oven for 7 to 8 minutes or until the bottoms are lightly browned. Cool on cookie sheets for 1 minute. Remove cookies to wire racks; cool completely.
For icing, stir together the sifted powdered sugar, 1 teaspoon vanilla, and enough milk (3 to 4 tablespoons) to make icing of drizzling consistency. Divide in half. Tint one half with drops of red food coloring.
Dip top third of each cookie into red-tinted powdered sugar icing for Santa's hat; place cookies on a wire rack and sprinkle a bit of coconut on edge of hat for fur trim and at the tip for a pompom. Dip bottom third of each cookie into white powdered sugar icing for Santa's beard, and return cookies to wire rack; sprinkle beard with coconut and allow icing to dry slightly. Place a cinnamon candy in center for a nose and two miniature semisweet chocolate pieces for eyes. Let dry completely. Makes about 42 cookies.
Store cookies in airtight container at room temperature up to 3 days. Or, freeze undecorated cookies up to 1 month; thaw and decorate as above.