Combine cabbage, green pepper, and onion in a large bowl. In a small bowl, whisk together mayonnaise, vinegar, powdered sugar, salt, and black pepper until smooth. Pour dressing over vegetables, tossing well to combine. Cover and chill at least 2 hours to allow everything to marinate.
When ready to serve, gently stir in tomato and season to taste with additional salt and pepper. (Chill, covered, up to 5 days.)
