Mix flour, baking soda and salt in medium bowl. Set aside. Beat granulated sugar and butter in large bowl with electric mixer on medium speed until light and fluffy. Add egg and lemon extract; mix well. Gradually stir in flour mixture on low speed until well mixed. Refrigerate 2 hours or overnight until firm.
Preheat oven to 375°F. Roll out dough on lightly floured surface to 1/8-inch thickness. Cut into shapes with cookie cutters. Place on greased baking sheets.
Bake 8 to 10 minutes or until lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.
For the Icing, mix all ingredients except food colors. (Stir in additional milk as needed to thin icing or more confectioners' sugar to thicken, if needed.) Place small amount of icing into small shallow bowls, using one bowl for each color desired. Stir drops of food color into icing until desired shade is reached. To ice cookies, hold cookie by its edge and dip top of cookie into icing. (Or spoon the icing onto cookie using a teaspoon.) Place iced cookies on wire rack set over foil-covered baking sheet to dry. (The foil-covered baking sheet will catch drips.) To add decorative details to cookies, spoon tinted icing into resealable plastic bag. Snip off a tiny piece of the corner. Squeeze icing through hole in plastic bag to decorate cookies. If desired, colored sugar may be sprinkled onto freshly iced cookies.