Does frost kill silver buttonwood shrubs?

Yes, frost could kill a silver buttonwood if the temperature reached below about 25 degrees Fahrenheit. Being planted in a courtyard or against a south-facing masonry wall might help protect it during a cold snap. Even if the top died, it might return from the roots even if the temps reached down to say, 20 degrees F. Silver buttonwoods are usually planted in USDA Zone 10 or warmer.