Whisk together cornmeal, flour, sugar, baking powder, 1 teaspoon salt, and 1 teaspoon pepper. Stir in eggs and milk. (You will have about 5 cups batter.) Fill a large heavy pot, Dutch oven, or deep fryer with enough oil to submerge hot dogs; heat until a deep-fry thermometer reaches 360 degrees.
Meanwhile, pat hot dogs dry, and insert a 10-inch bamboo skewer through each lengthwise; roll in flour to coat.
Dip 1 hot dog into batter, turning, until completely coated; let any excess batter drip off, and wipe away extra batter using your fingers so that hot dog is coated evenly. Lower hot dog into hot oil. Immediately repeat with 2 hot dogs.
Cook corn dogs, turning to cook evenly, until deep golden brown, 5 to 7 minutes. Transfer to a paper-towel-lined tray, turning to blot oil. Working in batches of 3, repeat with remaining hot dogs and batter.