Combine the wild rice with 3 cups of water in a saucepan.
Bring to a boil, then reduce to a simmer and cover. After 40 minutes, check to see if the wild rice is tender—because it's being used in a salad, you want it tender, but still maintaining its shape and some firmness.
Drain the rice, then stir in the vinegar and olive oil, and season with salt and pepper. Set aside.
To make the roasted root vegetables:
While the rice is cooking, preheat the oven to 400ºF and line a rimmed baking sheet with parchment paper.
Place the root vegetables on the baking sheet and drizzle with the olive oil. Toss to coat, then season with salt and pepper.
Roast the vegetables for about 45 minutes, stirring every 15 minutes or so, or until tender and beginning to brown on the edges.
To make the dressing:
Combine all ingredients in a small bowl and whisk until smooth, adding more water if needed.
Divide the wild rice and root vegetables into 4 bowls. Add the greens, dressing, and walnuts or pepitas and pomegranate arils, if using. Serve immediately.