Cream the butter and powdered sugar until it looks light and creamy. If it doesn't look creamy enough, you can add a few drops of heavy whipping cream.
Add the blue food coloring and mix well. Test that the frosting can form stiff peaks by turning a spoonful of it upside down - if it stays on the spoon, the frosting is ready. If not, add more powdered sugar in 1/2 cup increments and continue mixing.
When the frosting is ready, scoop it into a pastry bag (see pro-tip!) with a large tip and frost the cupcakes in a water design.
Repeat the process, replacing the blue food coloring with green, to get the color for the gators. Using a 13-inch round tip, form a capital "T" on top of the blue frosting, then place medium dollops on each side of the top of the "T" to make eyes. Place edible eyes in the center of each dollop. Add the gator's nose by putting another medium-sized dollop on the bottom end of the "T" and add two mini chocolate chips.
Pro-tip: If you don't have a pastry bag, you can use a Ziploc bag with one corner cut off as a makeshift one!