Cook the base mixture: In a large saucepan, combine the sugar, melted butter, and milk. Place over medium heat and bring to a gentle boil.
Boil without stirring: Let the mixture boil for 5–6 minutes, or until it reaches 225–230°F (soft-ball stage) on a candy thermometer. Do not stir during this time, as it can cause crystallization.
Prepare the dry mix: While the base is boiling, mix the oats, cocoa powder, and 1 cup of coconut in a large heatproof bowl.
Combine wet and dry: Carefully pour the hot sugar-butter mixture over the dry ingredients. Stir until everything is well coated and evenly mixed.
Chill until firm: Place the bowl in the refrigerator and chill until the mixture is firm enough to handle, usually 2–3 hours (or overnight for best results).
Roll into balls: Scoop portions of the mixture and roll them into 1 ½-inch balls using your hands.
Coat in coconut: Roll each ball in the extra coconut until fully covered. Place on a parchment-lined tray.
Store and enjoy: Refrigerate the snowballs until ready to serve. They can also be frozen for up to 3 months—delicious even when eaten straight from the freezer!