Didn't they change that, though? In the book, the line is "Jaime Lannister sends his regards", I believe. I thought the series ret-conned it so this was all Tywin's plan and Jaime had no part in it?
One point I started to allude to in my previous post but forgot to finish: when Benjen Stark brings Bran and Meera to the Wall and tells them he can't go any further, that the Wall has magic that prevents the dead from passing...if that's the case, unless the White Walkers have some magic of their own, or can destroy the wall, their army of wights cannot pass. The White Walkers could theoretically pass the Wall themselves and create a new army. And back in season one, wights were able to pass the wall, as the dead Night's Watch brothers became wights when Jon Snow saved the Lord Commander. I guess the technically were not wights yet, as the Night's Watch brought them back to Castle Black prior to them turning.
Yes, winter and the cold has to be one of the White Walker's greatest weapons. Think about Old Nan's stories of the Long Night, when families starved and killed their own as a mercy. It'll also be interesting to see if some of the visions that Dany saw in the House of the Undying come to pass; there was one vision of the Red Keep covered in snow and ice...it would be incredible to see the Long Winter make it all the way down to King's Landing.
Damn, another year's wait begins...