Place 9 cups Rice Chex cereal in a very large mixing bowl and set aside.
In a microwave-safe bowl combine 1 cup white chocolate chips, 1/2 cup smooth peanut butter, and 1/4 cup butter. Microwave on high for 1 minute and stir. If the mixture is not smooth, microwave in 15-second intervals, stirring after each, until smooth. Stir in 1 teaspoon vanilla extract.
Pour the melted mixture over the cereal and stir gently but thoroughly until the cereal is evenly coated.
Working in batches, transfer a portion of the coated cereal into a large resealable plastic bag. Add some of the 1 1/2–2 cups powdered sugar (use the powdered sugar across batches), seal the bag, and shake gently until the cereal pieces are evenly coated. Pour the coated cereal onto a baking sheet. Repeat until all coated cereal has been dusted with powdered sugar.
Spread the coated cereal in a single layer on the baking sheet and let cool until the coating is set and the cereal is no longer warm to the touch.
Once cooled, add 1 cup Lucky Charms Marshmallows, 1 cup small white chocolate–covered pretzels, and 1/2 cup green M&Ms to the coated cereal. Gently stir to combine.
Store the Muddy Buddies in an airtight container in the refrigerator.