Cream the butter, sugar, and vanilla thoroughly. Sift together the flour and salt, add to the butter, and mix. Fold in the nuts and cherries and chill the dough for 1 hour.
Preheat the oven to 400 degrees F.
Roll the dough into 1-inch balls and place on an ungreased cookie sheet (they do not spread as they bake). Bake until set but do not brown, about 10 minutes.
While still warm but set, roll the cookies in confectioners' sugar and cool. Roll in confectioners' sugar again and bake again for 10 to 12 minutes.