In a large mixing bowl, combine chopped wafers, sweetened condensed milk, walnuts, and rum; mix well. Chill 4 hours or overnight.
Dip palms of hands in powdered sugar; shape by teaspoons into 1 inch balls. Roll in powdered sugar. (If mixture becomes too soft, rechill). Cover and store in refrigerator. Reroll in powdered sugar before servbing, if desired.