Beat butter in large bowl with electric mixer at medium speed until smooth. Add powdered sugar; beat until well blended. Add egg and vanilla; beat until well blended.
Combine candied fruit and walnuts in medium bowl. Stir 1/4 cup flour into fruit mixture. Add remaining 2 1/4 cups flour to butter mixture; beat at low speed until blended. Stir in fruit mixture with spoon.
Shape dough into 2 logs, each about 2 inches in diameter and 5 1/2 inches long. Spread coconut evenly on sheet of waxed paper. Roll logs in coconut, coating evenly. Wrap each log in plastic wrap. Refrigerate 2 to 3 hours or overnight, or freeze up to 1 month (let frozen logs stand at room temperature about 10 minutes before slicing and baking).
Preheat oven to 350 degrees. Grease cookie sheets. Cut logs into 1/4 inch thick slices; place 1 inch apart on cookie sheets.
Bake 13 to 15 minutes or until edges are golden brown. Transfer to wire racks to cool.