Preheat the smoker to 250°F. Use a mild wood such as applewood. Line a rimmed baking sheet with foil or use a smoker-safe roasting pan.
In a large bowl, combine the ground venison, grated apple, diced onion, egg, breadcrumbs, milk, sage, salt, and black pepper. Mix gently until just combined. Shape the mixture into a compact loaf and place it in the center of the prepared pan.
In a separate bowl, toss the carrots, parsnips, and potatoes with the remaining olive oil, thyme, and smoked paprika. Arrange them around the meatloaf in a single layer so they roast evenly.
Smoke the pan until the center of the meatloaf reaches 160°F and the vegetables are tender, about 1 1/2 to 2 hours. Stir the vegetables once during cooking. If they soften before the loaf is ready, remove them and keep them warm.
Let the meatloaf rest for 10 minutes before slicing. Serve it with the roasted root vegetables.