Coleslaw: In a large bowl, toss together cabbage and carrots. In another bowl, whisk together mayonnaise, lemon juice, vinegar, horseradish, salt and pepper. Pour over cabbage mixture, stir to combine. Chill for 1 hour prior to serving and taste for seasoning, add additional salt, pepper or horseradish as needed.
Hot dogs: Grill jumbo hot dogs over medium-heat until they get a light char. Butter the hot dog buns and grill no more than a minute or two, as they will burn fast. Serve grilled hot dogs on toasted buns, covered with coleslaw.
Cook's Note: Also try adding chili over the hot dog, then top with coleslaw.