Heat a straight-sided medium skillet over medium-high heat. Add the oil; heat for another minute. Add the mushrooms and 1/2 teaspoon salt, and cook, stirring occasionally, until golden brown on all sides, about 5 minutes. Stir in the cranberries and walnuts; cook 1 minute more. Turn off the heat, add the arugula and another 1/4 teaspoon salt, and toss gently with the mushroom mixture to wilt.