How Do Bright Red Male Cardinals Survive?

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A male cardinal is the most common, North American animal of size that is virtually all red, a color used by few wildlife species. How do they survive so well in the wild with such a rare, flashy outfit that, even among the fully leaved trees of summer, seems to stand out like a sore thumb?

Hawks see red. Why, then, don't they decimate the population of male cardinals, which seem to do little to hide themselves, especially in winter when deciduous trees offer no leaves for cover.
How do red male cardinals survive?