Preheat the oven to 350°F and grease the bundt pan.
Buttermilk Cake
In a mixing bowl combine the flour, salt, baking powder, and baking soda and mix thoroughly. Set aside.
In a stand mixer, on medium high speed, cream butter and sugar until the butter lightens in color. Add eggs one and a time waiting a minute between each egg. Scrape down the sides as necessary. Add the vanilla. The mixture might look curdled but that is ok.
Reduce the speed to low and add half of the flour mixture and mix until just combined. Add the buttermilk until it is just combined and then add the rest of the flour mixture.
To color the batter optional: separate the batter into three different bowls. Mix each of the food colors into one of the bowls. Spoon the batter into the bundt pan to make the desired pattern. This can be dollops or following the design of the pan.
Place in the oven on the center rack. Bake for 60 minutes. About halfway through baking cover the cake with foil to prevent the bottom from getting too dark. Remove from oven when a toothpick inserted into the cake comes back clean.
Allow to cool on cooling rack until the cake comes to room temperature.
Making the eggnog buttercream
In the stand mixer beat the butter. Reduce the speed to low and add the powdered sugar. Once the sugar has been completely incorporated increase the speed to medium high and add the salt and eggnog. Beat until the buttercream gets pale in color and lighter in texture. Add more eggnog as desired.
Separate the frosting in to two bowls and color each with either red or green food color.
Pipe or pour and spread the icing onto the cake and dust with a little nutmeg.