In medium bowl, with electric mixer on medium, beat butter and sugar until light and fluffy. Beat in egg, corn syrup, lemon extract, and lemon rind until well-blended. Reduce mixer speed to low, and gradually beat in flour and salt. Gather dough into two balls; flatten each into a disk and wrap in plastic. Refrigerate dough at least 1 hour, or overnight. Soften dough slightly at room temperature before rolling out.
Separate candies by color, and place each color inside a plastic bag. Crush candies into small pieces.
Heat oven to 375°F. Line two large baking sheets with foil. Between two sheets of waxed paper, roll one disk to a 1/4-inch thickness. Using a 2-1/2- or 3-inch round cookie cutter or rim of glass, cut out cookies. Using 1-1/2-inch holiday cookie cutters, make cutouts in center of each cookie. Transfer cutouts to a separate baking sheet.
Transfer cookies to prepared baking sheets. Spoon ground hard candies into cookie cutouts, filling them completely to the same thickness as cookies. Sprinkle cookies and cookie cutouts lightly with colored sugars. Repeat with remaining dough disk.
Bake cookies and cutouts until firm and lightly golden and ground candies look translucent, about 5 minutes for cutouts and 7 to 10 minutes for cookies. Cool cookies completely on baking sheets. Using a thin metal spatula, carefully remove cookies from foil.