In a saucepan, gently bring to a simmer, the butter, sugar, and milk. Do not allow the mixture to come to a boil. Once the butter is melted and the sugar is dissolved, remove the saucepan from the heat.
In a large bowl, whisk together 3 1/2 cups of the coconut (set aside one cup for rolling the snowballs into later), chocolate cake mix, and rolled oats.
Poor the cooled butter mixture over the dry ingredients, and using a wooden spoon or spatula, mix the ingredients together until well incorporated.
The mixture will look gooey. Place the bowl into the refrigerator for a minimum of 2 hours.
Place the remaining one cup of coconut into a shallow, wide-set bowl. When the mixture has had time to set, use a small cookie scoop to portion out equal amounts of the cookie mixture. Roll the mixture into balls. Coat the balls in the remaining coconut by gently rolling the ball around.
Keep refrigerated. These snowballs are freezer friendly as well. Enjoy!