Soak your casings in a bowl of warm water. When they are soft, run water through them to check for leaks.
Chop the meat into pieces small enough to grind. Set the meat in the fridge. Chop the skin into small pieces, about 1/2 inch each. Set it in the freezer. When the skins are stiff but not rock hard, about 1 hour, grind them through the fine die of your grinder. Do the same for the meat. Check the temperature: If the meat and skin is anywhere below 35°F, you can proceed. If not, put it in the freezer until it gets cold enough.
You will now need to work fast, so have everything ready. When the meat and skin is between 28 to 32°F, put it into a food processor along with 1/2 of the ice water. Buzz it to emulsify, about 30 seconds to 1 minute. Add everything else to the food processor and emulsify that, which will take a minute or two. (If your food processor is not big enough to handle this job, you will need to split everything into two batches evenly. Keep the second batch of meat, skins and fat in the freezer while you work with the first batch.)
Put the mixture into the sausage stuffer, which you've been keeping in the fridge. Put the stuffer, now filled with your sausage, back into the fridge as you clean up. Take the stuffer out and stuff your casings.
Tie off links at whatever interval you want; I used hog casings here, and I made the links about 5-6 inches each. It is important to tie off your links with kitchen string, even if you normally twist off your links. The string prevents the links from unraveling when you poach them.
When all the links are tied, hang in a cool place while you get a big pot of water hot. As the water is heating, prick any air bubbles in the links with a pin or needle that you've sterilized in the stovetop's flame. When the water reaches 170 to 175°F -- this is below a simmer -- gently put the sausages in and poach for 25 minutes. Be careful to not let the water temperature get past 178°F, or the links can burst.
As the links are poaching, get an ice water bath ready. When 25 minutes are up, shock the sausages in ice water for 5 minutes.
Smoke over oak, applewood, etc. for 3-5 hours. It is important that your smoker be as cool as possible. I turn my Bradley smoker on, but leave the heater off. Once the links are smoked, let them cool on a rack for a couple hours, and then overnight in the fridge before you seal and freeze them. They will last 7-10 days in the fridge or indefinitely once sealed and frozen.