In a bowl, whisk together melted butter, hot sauce, vinegar, Worcestershire sauce, and garlic until well combined and set aside.
Heat a barbecue. Season the chicken with salt and pepper and cook the chicken for 30-40 minutes until cooked through.
In the meantime, combine the cabbages, carrots, mayonnaise, lemon juice, and mustard in a bowl and toss well.
When the chicken is cooked, spoon over some of the buffalo sauce. Serve the drumsticks with the remaining buffalo sauce and the coleslaw and some wedges on the side.
