Line a cookie sheet with parchment paper or a non-stick silicone baking mat. Combine white frosting and 1/4 cup white chocolate chips in a microwave-safe bowl.
Heat in 20 second increments, stirring between, until melted and smooth. If needed, you can add a teaspoon of shortening or coconut oil to soften the mixture.
Pour 1/2 cup confectioner’s sugar into a large gallon zip-top bag, then scoop in the white candy-coated cereal. Seal the bag and shake well until all of the cereal is coated with sugar.
Open the bag and shake out the cereal onto your prepared baking sheet, then repeat the process with green frosting to make the same amount of green Chex mix.