Preheat the oven to 325 degrees F. Line a baking sheet with parchment paper.
Place the cookie dough between two sheets of parchment paper. With a rolling pin, roll out the dough until it is about 1/4-inch thick. Set the rolled dough in the freezer for 15 minutes to firm.
Cut out cookies with a triceratops-shaped cookie cutter. Place the cookies roughly 2 inches apart on the parchment-lined baking sheet and freeze for 5 more minutes. Transfer the cookies and the parchment paper to a new baking sheet and bake until the bottoms are just golden brown and the centers are no longer doughy, about 15 minutes, rotating the baking sheet about halfway through baking.
Allow the cookies to cool for 5 minutes before transferring them to a cooling rack.
For the base coat, put about 6 ounces of the royal icing in a medium bowl. Add 5 drops of orange food color and 2 drops of yellow food color and stir with a rubber spatula to combine. Gradually add a teaspoon of water at a time until the icing is the consistency of thin yogurt; when you scoop some up with a spoon and let it drip back into the bowl, the lines should settle out. (Don't add too much water all at once; the icing should not be watery or it will run off the edges of the cookies.) Cover the bowl with a damp paper towel until ready to use.
Put 2 ounces of the royal icing in a small bowl. Add a few drops of water at a time until the icing is the consistency of thick yogurt. Transfer the icing to a disposable piping bag fitted with a coupler and a #1 round piping tip.
For the dark-orange spots on the dinosaurs, put about 3 ounces of the royal icing in a medium bowl. Add 5 drops of the orange food color and 1 drop of yellow and stir with a rubber spatula to combine. Add food color as needed until a shade slightly darker than the base coat is achieved. Add a few drops of water at a time until the icing is the consistency of thick yogurt. Transfer the icing to a disposable piping bag fitted with a coupler and a #1 round piping tip.
For the light-yellow outlines on the dinosaurs, put roughly 3 ounces of the white royal icing in a medium bowl. Add 3 drops of the yellow food color and stir to combine with a rubber spatula. Add food color as needed until a nice pale yellow is achieved. Gradually add a few drops of water at a time and mix until the icing is pipeable and slightly fluid, like thick yogurt. Transfer the icing to a disposable piping bag fitted with a coupler and a #2 round piping tip.
For the dinosaurs' eyes, put 2 ounces of white royal icing in a small bowl. Color the royal icing black by adding 2 to 3 drops of black food color. Stir to combine using a rubber spatula, adding a few drops of water until a thick yogurt consistency is. Transfer the icing to a disposable piping bag fitted with a coupler and a #1 round piping tip.
Once the cookies have cooled, flip the cookies upside down by holding the edge of the cookie. One at a time, dip the top of a cookie into the lighter orange base coat icing, moving the cookie slightly to make sure the top is coated entirely. The icing should not come up the sides of the cookies. Flip the cookie back over and jiggle the cookie slightly to help smooth out any lumps. Use a toothpick to pop any air bubbles and smooth out the icing. Place on the cooling rack and repeat with the remaining cookies until they are all coated.
Next, while the cookies are still wet, use the dark-orange icing to make 3 to 4 spots along the back of the triceratops and slightly above the legs. Allow the cookies to dry for at least an hour.
Using the white icing, pipe three small dots at the base of each of the two feet. Fill in the triangle shaped points sticking out of the head of the dinosaur to create two horns on each. Next pipe another horn on each that is the same size directly across from the horn towards the top of the head.
Pipe an eye with the black icing on each, creating a small curved line just between the two horns on the triceratops head.
For the border, pipe the light-yellow icing around the edge of each cookie, following the shape of the cookie. Next, pipe details to outline the legs, continuing the lines of the legs slightly upwards towards the body of the triceratops. Pipe what looks like a fishhook to create the mouths, swooping upwards towards the eye.
Allow the cookies to dry completely before serving.