Every now and then I have a pleasant dream where I can see, in my mind's eye, Jaime calling the banners and rallying every soldier he can find in the Westerlands to march them all north to Winterfell, answering the call for help against the Others.

I recommend it, as dreams go.

Anyway, if he does go north with 45,000 men, how would he be received? Does recently-alive Jon welcome him, or begrudge him coming in the first place? Do the wildlings know who he is? Does anyone care that he's a Lannister, more concerned with the soldiers behind him? Sansa might welcome him, and Brienne would be pleased to see him, but what about the Northern lords? Most importantly, would Jaime even care at that point, given the threat of the undead?