
In a large bowl, whisk together vinegar, sugar, and soy sauce; set aside.
Using a vegetable peeler or mandoline, thinly slice carrots, cucumbers, and daikon lengthwise into ⅛-inch-thick strips.
Transfer to bowl with dressing. Add radishes and salt; toss well.
Set aside to marinate 15 to 20 minutes, then serve. For a stronger flavor, marinate up to 3 days in the refrigerator.