I do it when I go hunting and it's cold sometimes, haven't had an issue. I generally try not to do it for extended periods of time. I'm no expert so take my opinion for what it's worth but I think you're probably alright.
My bows all hang in my shop, they have for over twenty years. I only heat the shop when I'm going to be out there, which isn't as much as I'd like. So, sometimes it's below zero out there for days at a time...never had a problem that I can say the cold caused.
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