In a medium bowl, combine cornmeal, flour, salt, pepper, sugar and baking powder. Stir in eggs and milk. Add more milk to adjust consistency for dipping.
Preheat oil in a deep saucepan over medium heat to 365°.
Cut each hot dog into thirds. Pat hot dogs dry with a paper towel and insert toothpicks into cut hot dogs. Roll hot dogs in batter until well coated.
Fry 4 to 6 corn dogs at a time for 1-2 minutes, or until lightly browned. Drain on paper towels. Place in a 200 F oven to keep the corn dogs warm until all are fried.
To make the honey mustard, in a small bowl, whisk together the mayonnaise, mustard, honey, and lemon juice. Serve with mini corn dogs for dipping.