Preheat the oven to 350Ëš F. Line 18 cupcake pans with paper liners.
In a medium bowl, combine the flour, baking soda, baking powder, salt and nutmeg; whisk to combine.
In the bowl of an electric mixer, combine the rum, eggnog, vegetable oil, vinegar, and sugar. Beat on medium-low speed until well blended.
Add in the dry ingredients and mix on low speed just until incorporated.
Divide the batter between the prepared cupcake liners, filling the cups 2/3 full. Bake 22-24 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool in the pan 5 minutes, then transfer to a wire rack to cool completely.
To make the frosting, place the butter in the bowl of an electric mixer fitted with the whisk attachment. Beat on medium-high speed until smooth, 20-30 seconds. Add in the powdered sugar, salt and nutmeg, and mix on medium-high speed until incorporated and smooth, about 1 minute. Scrape down the sides of the bowl. Add in the eggnog and whip on medium-high speed until light and fluffy, 4 minutes. With the mixer on medium-low speed, blend in the rum.
Fill a pastry bag with the frosting and decorate the cooled cupcakes as desired. Sprinkle with ground cinnamon or grated nutmeg, and garnish with cinnamon sticks if desired.