Preheat oven to 400°F. Beat butter and 1/2 cup confectioners' sugar in large mixer bowl until light & fluffy. Add water and vanilla. Gradually add flour & nuts, beating until well mixed. Refrigerate until firm, about 30 minutes.
Roll dough into 1-inch balls. Place 1 inch apart on ungreased cookie sheets.
Bake 10 minutes. Roll in remaining 1 cup confectioners' sugar. When completely cool, roll again in sugar.