A long time ago, she remembered her father saying that when the cold wind blows the lone wolf dies but the pack survives. He had it all backwards. Arya, the lone wolf, still lived, but the wolves of the pack had been taken and slain and skinned. - Arya Stark
The Cailleach might originate as an Ancient Mother Earth Goddess.
In the late medieval and contemporary folklore she is an ancient but ageless creature that personifies the supernaturals affect on the fertility of the land that often runs around in the form of a Hare.
The hare is a symbol of fertility and prophecy, it even replaces the man on the moon in traditional irish culture. Like the hare the Cailleach has children everywhere and she is a source of knowlege because shes been around so long she knows everything. Ive never heard the moon called the cailleach but theres probably a link in both their functions.
The Cailleach isnt just fertile she is super strong, she creates geographical features purely by heaving earth around or throwing huge boulders and everything enigmatic in the landscape is built by her. Round towers, passage tombs and dolmens for example.
Carlingford in County Louth is a Norse Gael place name meaning the inlet/Fjord of the Hag. But what its really interesting about it beyond the ethnic diversity is it describes the Cailleachs one flaw. She has to head into the water at places like Carlingford once every hundred years to renew her youth.
Unfortunately one day a mortal man interferes with her getting to the sea to renew herself because he wont look away to save her modesty while she runs into the sea naked and she dies. Stories like that might be about the conquering of feminine divinity in a male world or be about conquering the fertility of the land by agriculture.
She leaned her back against a fluted pillar and wondered if her brother was looking at the same stars tonight, wherever he might be. Do you see the white one, Quentyn? That is Nymeria’s star, burning bright, and that milky band behind her, those are ten thousand ships. She burned as bright as any man, and so shall I. You will not rob me of my birthright!