Heat oven to 375 degrees F.
Beat butter and 34 cup confectioners sugar in large bowl until fluffy, 1 minute. Beat in vanilla. Stir in flour, salt and hazelnuts to make stiff dough.
Using about 2 teaspoons dough for each snowball, roll into balls with hands. Arrange on ungreased baking sheets, spacing 1-12 inches apart.
Bake in 375 degree F oven 12 minutes or until pale golden on bottoms.
Sift about one quarter of remaining confectioners sugar (a heaping 12 cup) into a 13 x 9 x 2-inch dish. Add a baking sheet of hot cookies to sugar in dish. Sift another heaping 12 cup confectioners sugar over them. Let cool in sugar to coat. Repeat with second half of cookies and remaining sugar.
Once cookies have cooled completely, serve, sifting any extra confectioners sugar from dish over cookies. Makes about 4 dozen cookies.