Preheat oven to 350 degrees F. Lightly coat thirty-six 1-3/4-inch muffin cups with nonstick cooking spray (or line muffin cups with paper bake cups); set aside.
In a medium mixing bowl, combine white cake mix, the 1/2 cup eggnog, egg, the 1 teaspoon vanilla, and nutmeg. Beat with an electric mixer on low speed until just combined. Beat on medium speed for 2 minutes until well combined, scraping side of the bowl often. Divide batter evenly among the muffin cups, filling each about two-thirds full (about 1 rounded teaspoon in each). Bake in preheated oven for 10 to 12 minutes or until a toothpick inserted near the center comes out clean. Cool cakes in pan for 5 minutes. Remove cupcakes from muffin cups and place on a wire rack. Cool completely.
To tint coconut, if desired, combine some of the coconut and several drops of red or green food coloring in a small resealable plastic bag. Seal bag. Using your hands, knead the bag until all coconut is tinted, adding more food coloring as necessary to reach desired color. Set tinted coconut aside.
For frosting, in a medium mixing bowl, beat cream cheese and butter with an electric mixer on medium speed until well combined. Beat in powdered sugar and the 1/2 teaspoon vanilla. Beat in enough eggnog (1 teaspoon at a time) to make a frosting of dipping consistency.
Dip tops of cooled mini cupcakes in cream cheese frosting. Immediately dip frosted tops into plain or tinted coconut. Set cupcakes upright.