Preheat oven to 375 F. Beat butter at medium speed with electric mixer until soft and creamy, gradually add confectioners' sugar, beating well after each addition. Add vanilla and flour, mixing well. Stir in oats and chopped nuts. Shape dough into 1-inch balls. Place on ungreased cookie sheet. Bake for 12 minutes. Remove from pan. Roll balls in confectioners' sugar and cool on wire racks.