In a large bowl, cream together the butter and sugar. Beat in the rum and eggnog.
Add in the flour mixture gradually until well-combined. Cover and refrigerate the dough an hour or until firm.
Preheat the oven to 350 degrees and line two baking sheets with parchment paper. Roll the dough into 1″ balls and place on the baking sheets about 1″ apart.
Bake 12-14 minutes. Remove to a wire rack to cool about 5 minutes before rolling the cookies in the sugar. Makes about 3 dozen cookies.