In a saucepan, combine the Brussels sprouts, apple juice, water and 1 teaspoon salt. Bring to boil over medium-high heat, reduce the heat to low, cover, and cook just until the sprouts are tender yet firm when pierced at the base, about 15 minutes. Drain well.
Cut pumpkin flesh or butternut squash into cubes and roast in a pan. Put aside in a bowl.
Cut the Brussels sprouts lengthwise into thin slices. Add the slices to the pumpkin cubes or butternut squash and mix them gently together with fat-free dressing.
Divide the arugula among individual plates. Spoon the vegetables over the arugula and garnish with the chopped walnuts. Serve while still warm.