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Your hair loss, or the Deer hair loss?!!
She will survive just fine. I've seen some of them go nearly completely bald and survive all winter. If they are bald and we got a cold snap from Alaska, then some of them would freeze to death but a mild winter won't kill them. This time of year they are fine and once they get over it, they are more immune to it.
I would think that if it was gonna kill her, it woulda happened during winter. I've seen lots of deer with patchy coats when they shed in spring, but that one is way beyond spring shedding.