Combine the salt and water in a 4-quart container and stir until the salt has dissolved, 1 to 2 minutes. Add the trout filets, making sure they are submerged. Cover and refrigerate for 3 hours.
Remove the trout from the brine, rinse thoroughly, and pat dry. Place the trout, skin side down onto a cooling rack set in a half sheet pan. Dry in the refrigerator 21 to 24 hours or until the skin becomes shiny and somewhat tacky to the touch.
The next day, turn the smoker on so that it maintains a temperature of 150 to 160 degrees F. Place the trout onto smoking racks, skin side down, separating them by at least 1/4-inch and place into a smoker. Adjust heat as needed and cook for 2 1/2 to 3 hours or until the fish is, cooked through, has darkened in color, and has the desired level of smoke flavor.
Serve with a green salad, incorporate into a dip or eat as an appetizer. Refrigerate unused portions in an airtight container for up to a week or vacuum seal and refrigerate for up to a month.