Heat oven to 325 degrees. Prepare a tube pan by coating with cooking spray and dusting with flour.
Using a stand or hand mixer, cream butter and shortening together. Mix in sugar and whip until light and fluffy. Add in eggs, one at a time, blending thoroughly. Continue to mix while adding in nutmeg, cinnamon and vanilla.
With beater running, add flour and eggnog alternating into sugar mixture, starting and stopping with flour. Pour into prepared 10 inch tube pan. Bake for approximately 1 hour and 15 minutes. Test for doneness by inserting a skewer that should come out clean when cooked completely.
Let cake cool for 20 minutes then remove from pan. When cake is completely cooled, store covered.
In a small bowl, mix together confectioners sugar and eggnog until smooth. Drizzle over cooled cake.