Stir cold water, curing mixture, liquid smoke, mustard seed, garlic powder, and black pepper in a large bowl until curing mixture is dissolved. Mix in venison, Cheddar cheese, and jalapeño peppers until evenly blended and somewhat sticky, about 3 minutes. Divide mixture in half, then roll each half into 2-inch-thick logs. Wrap each log tightly with aluminum foil and refrigerate for 24 hours.

Preheat the oven to 300 degrees F (150 degrees C). Line a baking sheet with aluminum foil.

Remove foil from sausage logs and place them onto the prepared baking sheet.

Bake in the preheated oven until an instant-read thermometer inserted into the center of sausages reads at least 160 degrees F (72 degrees C), 1 1/2 to 2 hours. Cool sausages on a rack to room temperature. Dab occasionally with a paper towel to absorb excess grease. Slice thinly to serve.