Preheat the oven to 325 degrees. Line cupcake tins with liners.
Beat the oil, sugar, and red food coloring in the bowl of a stand mixer on low speed for 5 minutes. Scrape the sides and bottom of the bowl.
Add the eggs one at a time, beating well after each addition.
Combine the dry ingredients in a separate bowl and stif with a wire whisk to mix.
Combine the buttermilk, vanilla, and vinegar in a large liquid measuring cup.
Alternately add the dry ingredients and the buttermilk mixture to the mixing bowl, starting and ending with the dry ingredients, beating until well blended. Scrape the sides of the bowl and incorporate any unmixed batter if necessary.
Pour batter into lined cupcake tins about 2/3 full. Bake 20-25 minutes or until a toothpick inserted into the middle of a cupcake comes out clean. Cool the cakes completely before icing.
To prepare the cream cheese icing: Cream the butter and cream cheese in the bowl of a stand mixer for 3 minutes. At the end of the 3 minutes. scrape the bowl extremely well. Add the vanilla extract, black food coloring and beat for 1 to 2 minutes. Slowly add the confectioners' sugar, beating on low to ensure the sugar does not fly out of the mixing bowl. After each addition of confectioners' sugar, scrape the bowl extremely well. After all confectioners' sugar is incorporated, beat on low speed for 3 minutes. Using an offset spatula, of flat metal spatula, ice the cupcakes with grey icing. Once the icing is slightly set, use a straw to make "plates" across the top of the cupcake.
To make tails: Working with 1 at a time, place a tootsie roll in a glass bowl and microwave until warm and barely soft, about 5 seconds. Roll the warm tootsie roll into a long-pointed tail. While warm, use a toothpick to notch and create the tail plates. Press larger end of the tail into the cupcake to give an armadillo look.