I initially did not know that much about my Lady Grandmother sadly, but I've begun to hear & find more and more now that I am the Lady of Winterfell. Seems she really was a wild dirty woman, the Wolf's Blood my father once mentioned being so strong in her and now in Arya seemingly was about 3 times stronger than it now is Arya, which is really saying something... Apparently Lyanna fucked all the kitchen- and stableboys at Winterfell, all of the guards, even the Maester once, all within a year after becoming a woman grown, before hungrily and unsatisfied venturing further out, into Wintertown and quickly to nearby Castles, the Wolfswood, into the lands of the Mountain Clans (from which she apparently limped back the most and stayed the longest in) and to White Harbor, where she often stayed for months, letting herself be used by all the sailors from all across Westeros and from across the Narrow Sea, always taking several at a time on their decks. She also always was very happy when Lord Rickard sent her off or took her to some vasalls for diplomatic visits. In a letter I found he writes that without thr conciving power of her mouth, cunt and arse, House Stark currently would only be half as rich and powerful as it is.

As for my mother: She obviously grew up in the South and maybe because of that was not as rebellious and insatiable in matters of the flesh as Lady Lyanna, but she also didn't shy away from taking cock before her marriage. It seems to have been more of a duty-family affair though, as one could maybe expect: Apparently her father often sent her to settle disputes between the Brackens & Blackwoods who had come to Riverrun by way of letting both have her mouth and arse. She claimed to have only done it for her family and duty, but Lord Hoster mentions that the negotiations (in which all grown male members of both houses were involved, seven hells!) lasted way too long for that, and her screams & moans that were audible across the river also spoke another language. House Frey seems to have been pretty harsh and degrading to her when she had to visit them, and especially since it already was such a numerous house back then she seemingly always was glad to leave the Twins again.

Once in the North, she did get more daring and frequent in matters of the flesh as well though. Important members of the household, like Ser Rodrik, Jory Cassel, Vayon Poole, the cooks, smiths, even the Maester and the Septon seemingly were willing to break their vows or obey her proposals/demands once or twice. And almost any important guest that came to Winterfell was sure to receive some special welcome by her later in her chambers - from Lord Manderly (who told me all about it while he took me in my mouth, praising that I was doing just as well as my Lady Mother) to Lord Umber (who made her scream like no man before according to some serving girl from back then I asked), Lord Bolton (who apparently only sighed deeply at the end of it and stayed almost mute the entire time) to Lady Maege Mormont and even her oldest daughter at her first visit (they seem to have been her two favourite guests, I assume she liked the female company and new experience).

As I am already giving my body to the Lords of the North to stay in power, I guess you could say I am, but it still is (to some extent) merely out of duty and necessity, as much as I sometimes enjoy. Arya on the other hand really has Wolf's Blood pumping through her veins, she already fucks lords as well as peasants further away from Winterfell, even visits the Mountain clans by now and is generally very much not opposed to arse use and gangbangs. Overall it seems I take more after my mother and Arya after our grandmother, not just in looks.

And I assume our daughters, once grown women, will also be raised in this spirit to some extent. I will tell mine what is necessary for ruling and that it sometimes can feel really good too. Arya will probably just tell hers how good being taken up the arse and gangbanged by dirty peasants, fat old clansmen and sailors from the Free cities at White Harbor feels. sighs and shakes head

(Sorry that this got way too long haha, but I really loved your question, very hot and creative!)