Put the potatoes in a large pot and cover with water by 2 inches; season generously with salt. Bring to a boil, then reduce the heat to a simmer and cook until just tender, 10 to 12 minutes. Drain and transfer to a large bowl. Drizzle with the vinegar and sprinkle with 1 teaspoon salt; gently toss to coat. Let cool.
Meanwhile, bring a medium saucepan of salted water to a boil. Add the snap peas and cook until bright green but still crisp, about 1 minute. Transfer to a bowl of ice water and let cool, then drain and pat dry. Slice the peas in half.
Whisk the mayonnaise, sour cream, horseradish, mustard, 2 tablespoons water, the lemon zest, 1 1/2 teaspoons salt and 1/2 teaspoon pepper in a medium bowl. Add to the potatoes along with the snap peas, celery, dill, parsley and chives. Gently stir to combine. Cover and refrigerate until ready to serve.