In a medium mixing bowl beat together sour cream, cream cheese, mayonnaise, soy sauce, horseradish (if using), salt, and pepper with an electric mixer until smooth. Stir in shredded carrots and green onions until combined.
Cover and chill for 4 to 24 hours (do not prepare further ahead than this or the dip will become too thin). Keep the dip chilled while transporting. Stir dip before serving with dippers. Makes 2 cups (about 10 servings).