Whisk the cornmeal, flour, sugar, baking powder, mustard powder and 1 1/2 teaspoons salt in a large bowl. Whisk the milk, eggs and peanut oil in another bowl, then add to the cornmeal mixture and whisk until smooth. Pour the batter into a tall drinking glass, reserving any extra batter.
Heat 3 to 4 inches peanut oil in a large, wide saucepan over medium heat until a deep-fry thermometer registers 365 degrees F. Spread some flour in a shallow dish. Thread each hot dog three-quarters of the way onto an 8-inch wooden skewer. Dredge the hot dogs in flour, tapping off the excess.
Working in batches, dip the hot dogs into the glass of batter; let the excess drip back into the glass, then lower the hot dogs into the hot oil. Fry, turning, until golden, 4 to 5 minutes per batch. (Refill the glass with batter as needed.) Remove the corn dogs with tongs and drain on a paper towel-lined plate; season with salt.