In a small bowl, whisk together vinegar, mustard, salt and pepper. Whisk in oil in a steady stream, until emulsified. (Dressing may be made up to 1 week ahead; cover and refrigerate.)
Using a small sharp knife, remove a thin slice from top and base of each orange. Set each fruit on its base and cut from top to bottom to remove both rind and white pith in thick strips. Working over a bowl, cut between membranes to release orange sections, removing seeds as you go. Reserve juice for another use.
Combine oranges, watercress and radishes in a serving bowl. (Salad may be prepared up to 4 hours ahead; cover and refrigerate.) Toss salad with dressing just before serving.