In a small bowl, cream butter and brown sugar until light and fluffy. Beat in egg. Beat in the applesauce, vanilla and orange zest. Combine the flour, baking powder, salt and baking soda; gradually add to the creamed mixture until well combined. Stir in pecans.
Fill paper-lined muffin cups half full. Bake at 350° for 20-25 minutes or until a toothpick inserted in the center comes out clean. Cool for 10 minutes before removing from pan to a wire rack to cool completely.
For frosting, in a small bowl, cream butter and confectioners' sugar until light and fluffy. Add the orange zest, food coloring and enough orange juice to achieve spreading consistency. Set aside 1/4 cup orange frosting. Frost cupcakes.
Transfer chocolate frosting to a heavy-duty resealable bag; cut a small hole in a corner of bag. Pipe a circle of chocolate in center of each cupcake. Pipe evenly spaced thin concentric circles about 1/4 in. apart. Beginning with the center circle, gently pull a toothpick through circles toward outer edge. Wipe toothpick clean. Repeat to complete web pattern.
Cut licorice into 2-in. pieces; press eight pieces into each gumdrop for legs. Place reserved orange frosting in a heavy-duty resealable bag; cut a small hole in a corner of the bag. Pipe eyes on each spider gumdrop. Position on cupcakes.