Preheat oven to 350 degrees. Lightly grease cookie sheets.
In a bowl, using a mixer, combine melted butter, sugar, flour, vanilla, walnuts and pinch of salt and mix until a stiff dough forms. Shape dough into 1 inch balls and place on prepared cookie sheets. With your fingers, slightly flatten each ball.
Bake in preheated oven for 15 minutes. While still warm, roll each snowball in sifted confectioners' sugar. Place on wire racks to cool. When cookies have cooled completely, roll in confectioners' sugar again. Makes about 6 dozen. Enjoy!