For the cupcakes: Preheat the oven to 350 F. Prepare three 12-cup standard muffin tins with cupcake liners.
Add the oil and eggs to a large bowl and beat with a hand mixer until lighter in color. With the mixer running, add the granulated sugar, cinnamon, salt, baking soda and vanilla, until well combined. Add the flour to the bowl and mix just until incorporated. Fold in the coconut, walnuts, pineapple and carrots with a rubber spatula. Scoop about 1/4 cup batter into each cupcake liner and bake two of the tins, switching and rotating the position of the tins halfway through, until deep golden, 15 to 18 minutes. Cool completely in the muffin tins on a rack. Bake and cool the remaining tin in the same manner.
For the frosting: Meanwhile, cream the butter, cream cheese and powdered sugar together in a large bowl with a hand mixer until light and fluffy. Add the vanilla and salt, then add the milk 1 tablespoon at a time until the desired consistency is reached. Top each cupcake with about 2 tablespoons frosting and swirl with the back of the spoon. Top with freshly grated nutmeg.