Preheat your oven to 375°F (190°C) and prepare a baking sheet by lining it with parchment paper or a silicone baking mat.

In a large mixing bowl, combine the cake mix, eggs, vegetable oil, and vanilla extract, stirring until a dough forms.

Divide the dough evenly into two small bowls. Add red food coloring to one portion and green food coloring to the other, mixing thoroughly until the colors are vibrant and consistent.

Chill the colored dough in the refrigerator for at least 30 minutes to enhance its workability and improve the cookies' texture.

Use a tablespoon-sized cookie scoop to portion the dough. Roll each piece into a ball, then coat generously in powdered sugar. If the dough is too sticky to handle, incorporate about one tablespoon of flour into the mixture and mix well.

Arrange the sugar-coated dough balls on the prepared baking sheet, leaving adequate space for spreading.

Bake in the preheated oven for 9 to 11 minutes, or until the cookies have set and the crinkle pattern has formed.

Allow the cookies to cool for 1 to 2 minutes on the baking sheet before transferring them to a wire rack to cool completely.