First, make the vinaigrette: place all of the vinaigrette ingredients in a medium bowl and whisk until emulsified. (Alternatively, place all the ingredients in a mason jar, close tightly, and shake vigorously until emulsified.) Refrigerate until needed. The vinaigrette can be made well in advance and will keep, refrigerated, for up to a week.
In a large serving bowl, gently toss together the endive, radicchio, mixed baby greens, and apple pieces. Drizzle with approximately half the vinaigrette, toss again, and add additional vinaigrette as needed until the salad is lightly and evenly coated. Sprinkle with the pomegranate seeds and walnuts, and serve immediately. (If making ahead, do not dress the salad until serving time to keep the greens from wilting.)