To prepare cookies, beat granulated sugar and margarine in a large bowl at medium speed of a mixer until well-blended (about 4 minutes). Add egg and next 4 ingredients (egg through 1 teaspoon vanilla), beating well. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 4 ingredients (flour through salt). Add flour mixture to sugar mixture, stirring well. Spoon dough onto plastic wrap; flatten to a 1 1/2-inch thickness. Cover tightly with plastic wrap; chill 4 hours or overnight.
Preheat oven to 400°.
Roll dough to a 15 x 12-inch rectangle on a heavily floured surface. Cut dough into 20 (3-inch) squares using a sharp knife. Place cookies 2 inches apart on ungreased baking sheets. Bake at 400° for 8 minutes or until golden. Immediately remove cookies from pans using a wide spatula, and cool on wire rack.
To prepare icing, combine powdered sugar, 1 tablespoon milk, lemon juice, and 1/4 teaspoon vanilla. Stir in food coloring, if desired. Spread about 2 teaspoons of the icing over each cookie, or place icing in a small zip-top plastic bag. Snip a tiny hole in one corner, and drizzle icing over cookies. Sprinkle with assorted sugar sprinkles, if desired.