Preheat oven to 400°F.
Cream confectioners' sugar, butter and salt in large bowl. Add vanilla. Gradually add flour to creamed mixture. Stir in nuts. Refrigerate until chilled, about 1 hour.
Form into 1-inch balls. Place on ungreased cookie sheets. Bake 8-10 minutes until set but not brown. Roll in confectioners' sugar immediately. Cool on rack. Store in airtight container.
Makes 3 dozen cookies.
Quick Tip
Pastel-Tinted Snowballs can be made by rolling cookies in colored sugar. To tint sugar: place 1 3/4 cups confectioners' sugar into blender or food processor. Drop several drops of food coloring into center of sugar; blend briefly. Pink, green and yellow sugars make pretty snowballs.