Pour oil to a depth of 1/2 inch into a large heavy skillet. Fry won ton strips in batches in hot oil over medium-high heat until golden. Drain on paper towels, reserving drippings in skillet; set strips aside.
Sauté ginger in reserved drippings until crisp; drain on paper towels.
Cut cabbage, carrot, and snow peas into thin strips; place in a large salad bowl. Add ginger; drizzle with Sesame-Soy Vinaigrette, tossing gently. Serve with won ton strips.