Bring rice and water to the boil in a saucepan over high heat. Reduce heat to medium-low, cover and cook until the rice is tender, about 40 minutes.
Meanwhile, place squash, cut-side down onto a deep baking dish filled with 1.25cm of water. Bake in preheated oven for 40 minutes, then drain water and set aside.
Bring some water to the boil in a saucepan, then remove from the heat. Add the cranberries and let stand for 5 minutes, then drain and reserve. Cook the minced venison in a frying pan over medium-high heat until thoroughly cooked and crumbly.
Stir together the wild rice, cranberries, venison and dark brown soft sugar. Season with cinnamon, nutmeg, salt and pepper.
Preheat the grill. Rub the inside of the squash halves with the butter, then place cut-side up on the baking dish. Stuff with the rice mixture, then grill in the oven for 5 minutes.
If acorn squash is unavailable, feel free to use butternut squash.