I've been thinking about which consequences the war with the Others will have on Westerosi society, and I've come up with comparing the development to the end of post-Second World War Germany. Like any comparison, it won't work completely, but it may be a beginning.
First of all, one should consider that the society of pre-WWII society was a bit more flexible when it came to social rise and decline than the Westerosi society, but it's in no way comparable to today's situation. It was common to die in the class you were born into.
Now, what happened at the end of WWII? Of course, many people had died by then, leaving certain positions empty. Many people - also old elites - lost their homes, either from the bombings or because they were driven away from their home regions/expropriated.
After that, those parts of the old elites who were lucky and managed to escape the fate of becoming refugees, were at least partly able to keep/re-establish their social positions, because there were education, possessions, and old networks in the background. Refugees who got expropriated and who were driven away from their home region lost everything, including their old contacts, so permanent social decline was possible.
At the same time, so much was destroyed and so many positions were vacant that social rise in society was possible, too. You had to have some competences: education/quick apprehension, flexibility, energy, survival & business instincts, and often enough, a certain ethical shadiness was helpful, too.
Considering all these aspects, one can say that there was an increased social flexibility after WWII.
Let's switch to Westeros now. We've got a rigid class system there. Social rise and social decline are comparatively rare and if they happen, they're usually linked to a ruler's wrath or generosity. Rare examples of social rise are the Clegane family and Petyr Baelish. When we look at Baelish, there are some parallels to things I've mentioned above: education/quick apprehension, flexibility, energy, business instincts, and a certain ethical shadiness. When it comes to the Cleganes, it's Lannister support that has made their social rise possible.
However, there are still limits as to how far you can rise, especially within 1-3 generations. Petyr ruthlessly tries to push these boundaries, and with some temporary success, but even these men notice the social glass ceiling at every turn. There are things they simply can't do without having to fear repercussions from the establishment.
So what will the apocalypse of the ice zombies in the North mean for the Westerosi society?
There are already many vacancies from the previous wars, and there's destruction almost everywhere on the continent. Add to that deprivation from an extremely long and harsh winter. Then add the havoc caused by invaders (Dany, ice zombies...).
In book canon, we can already see how wildlings enter the Seven Kingdoms and are integrated at the Wall (we know the price Jon Snow has to pay for this, but still - it happens). I believe that these tendencies will continue and increase.
I think we'll witness great changes in the Westerosi society. The established, rigid system will crumble (perhaps alongside with the Wall?), and there will be a phase of great fluctuation where things will become possible that haven't been possible before.
If we believe show canon, upstart Petyr Baelish is doomed. I keep wondering what will happen to Sandor Clegane, and I keep asking myself which parts of the old elites might survive - and under which altered circumstances. I'm pretty sure GRRM will come up with interesting ideas.