Answer: Nandina will not be cold-hardy in your gardening region unless you can provide some winter protection. Planting next to the foundation of a house will help somewhat; a west-facing site will protect the plant from dessicating winds and close proximity to your home will help radiate heat during the coldest months. Still, there's no guarantee.
Before planting any shrub, I'd suggest amending your heavy clay soil with organic matter to help loosen it up (for good root penetration) and help it drain quickly.
Best wishes with your landscape!
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