Slice both red and green apples into thin matchsticks, then toss them with lemon juice to keep them from browning and to add brightness. Let them sit for 5 minutes.
In a large bowl, combine the matchstick carrots, finely diced yellow onion, and dried cranberries. These provide crunch and contrast.
Add the lemon-coated apples into the bowl and mix gently to combine.
In a separate bowl, stir together the yogurt, mayonnaise, sugar, salt, and black pepper. Pour over the salad and fold gently until coated.
Carefully fold in the mandarin orange segments without breaking them.
Cover and refrigerate for at least 3 hours before serving. Serve cold.
