Technically they can't die at all on account of not being alive. But no, they don't. In fact they seem to be more structurally stable at cooler temperatures, though that may vary with species. The freeze-thaw process of water can destroy them, and the more times it occurs, the more are destroyed.
In fact, the avian flu cycle may be perpetuated by virus particles released during the spring thaw. And ancient viruses may wait in permanently frozen water such as the most northerly lakes. They might be released by global warming. We can only hope that the fact that hardly anyone lives near them keeps such strains contained.
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