In large bowl, beat together butter and sugar with electric mixer on medium speed until light and fluffy, about 3 minutes. Add eggs, one at a time, mixing well after each addition. Add eggnog, rum (optional) and vanilla.
Roll dough out on a lightly floured surface to 1/4-inch thickness. If dough seems sticky, use additional flour and knead into dough. Using floured cookie cutters or a round biscuit cutter, cut into desired shapes.