His time scales are screwy.
I don't mean the seasons/years things. If this were SF, I would say the planet has an eccentric orbit or a variable primary. Being fantasy, I'm just rolling with the whole summer/winter business. It's integral to the story. But it's pretty clear in the text that a very long-lived human being could hope to make a 100 years of age -- not dissimilar to our own lifespans, though perhaps a bit extreme for the qua-Medieval medicine and nutrition enjoyed by this culture. Yet individual families (the Starks, for example) are said to have ruled for 8,000 years.
What was your family doing 8,000 years ago? What are any of the great (or small) families of that age doing today? Outside of China, I'm not sure there's reliable lines of direct descent and inheritance going back 2,000 years in our culture. Even in China it's not much further. How in the world can a human culture remain static for 8,000 years? Maybe there's an answer waiting later in the series, but I've about decided that it's like that line in Star Wars about the Jedi protecting the Republic for a thousand generations. Intended to sound cool and confer a sort of "myth of the Golden Age" overtone, it instead bespeaks a cultural stasis that is deeply frightening, and would be death of any ordinary human beings.