In a mixing bowl, combine 1 1/2 cups of flour, sugar, salt, yeast and nutmeg; set aside. In a saucepan, heat eggnog and butter to 120-130 degrees (the butter doesn't need to melt all the way); add to flour mixture. Beat on low until moistened; beat on medium for 3 minutes. Stir in cranberries and enough remaining flour to make a soft dough. Turn onto a floured surface; kneed until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about an hour. Punch dough down; divide into thirds. Shape each third into a 16-inch rope. Braid ropes on a greased baking sheet; seal ends. Cover and let rise until nearly doubled, about 30 minutes. Bake at 350 degrees for 25-30 minutes or until golden. Immediately remove from pan to a wire rack to cool completely.
Combine the first three glaze ingredients; drizzle over braid. Dust with nutmeg.