Core apples and cut into thin slices; cut slices into matchsticks (you should have around 3 1/2 cups julienned apples). Place in a large bowl and toss with lemon juice. Add carrots and stir to combine.
In a small bowl, whisk together mayonnaise, yogurt, honey, rice wine vinegar, and salt and pepper, to taste. Pour over apple/carrot mixture and stir to coat. Mix in crumbled feta cheese and dried cranberries. Taste and adjust seasonings, adding more salt and pepper, if necessary. Refrigerate for at least 30 minutes to an hour to allow the flavors to blend, or longer if you prefer softer carrots and apples. If a bit of liquid accumulates at the bottom of the bowl, serve using a slotted spoon.
You may use all yogurt or all mayonnaise if you prefer, but realize that doing so will slightly affect the flavor of the dressing.Same thing goes for the honey...tweak it up or down depending on how sweet you prefer your slaw.You can typically buy pre-cut matchstick carrots in the produce section of the grocery store. Try to cut your apples about the same size.