Preheat oven to 350°F. Spray large rimmed baking sheet with nonstick spray. Combine squash, rutabagas, and sweet potatoes in large bowl. Add oil and cayenne and toss to coat. Sprinkle with salt and pepper. Spread vegetable mixture on prepared baking sheet. Roast until vegetables are tender, stirring and turning occasionally, about 1 hour. (Vegetables can be prepared 4 hours ahead. Let stand on baking sheet at room temperature. Rewarm in 350°F oven until heated through, about 15 minutes.)
Transfer vegetable mixture to bowl. Add red onion, chives, and vinegar; toss to blend. Season with salt and pepper.
