To toast the pecans, place them in a skillet over medium heat. Toast, stirring often, until golden on the edges, about 4 to 5 minutes. Remove from heat. If you used whole pecans, roughly chop them. Set aside.
Arrange the arugula across a large serving platter. Sprinkle the chopped pecans and crumbled goat or feta cheese over the arugula. Fan out the apple and pear slices, arranging them across the salad in sections. Sprinkle with pomegranate arils evenly across the salad.
When you are ready to serve, combine all of the dressing ingredients and whisk until blended. Taste and, if necessary, add additional vinegar. Drizzle the dressing lightly over the salad and serve.