1. Prepare the Meat and Fat:
To ensure a smooth grinding process, make sure your pork shoulder and fat are cold. Cut the pork and fat into small, manageable cubes. This will make grinding easier and help in achieving the perfect texture for your sausages.

2. Grind the Meat:
Using a meat grinder fitted with a medium or fine plate, pass the cubed pork and fat through the grinder. This step is crucial for achieving the right consistency for your hot dogs.

3. Season the Meat:
In a large mixing bowl, combine the ground pork, fat, kosher salt, black pepper, paprika, garlic powder, onion powder, ground mustard, ground coriander, and ground nutmeg. Mix thoroughly to ensure the seasoning is evenly distributed throughout the meat. 

4. Add the Water:
Gradually add the ice-cold water to the seasoned meat mixture. Mix well until the mixture becomes sticky and well-combined. The water helps in binding the meat and ensures a smooth texture for the sausages.

5. Prepare the Casings:
Rinse the natural sheep casings thoroughly to remove any salt. Soak them in warm water for at least 30 minutes to make them pliable. After soaking, rinse the casings again and run water through them to check for any holes or weak spots.

6. Stuff the Sausages:
Attach a sausage stuffing attachment to your meat grinder or use a standalone sausage stuffer. Carefully thread the sheep casings onto the stuffing nozzle. Begin stuffing the sausage mixture into the casings, being careful not to overstuff. Twist the sausages into hot dog-sized links, about 6 inches long.

To cook the sausages, you can poach them in gently simmering water (about 160°F to 170°F) until they reach an internal temperature of 150°F. This usually takes about 20-30 minutes. Alternatively, you can grill or pan-fry the sausages over medium heat until they are cooked through and nicely browned.

Once your sausages are cooked, serve them in buns with your favorite toppings. Classic choices include mustard, ketchup, relish, onions, and sauerkraut.