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Many of the events before 6,000 years ago in Westeros, during the Age of Heroes, are half-legendary, and some of the more fanciful tales of these times probably have little basis in reality.
Still, all legends and oral histories may have some kernel of truth behind them. Martin himself, is that as the saying goes, history tends to be written by the victors.
Less than a full year actually passes in each novel.
The child actors in the TV series, however, still age at a normal rate during production, so in order to keep consistent, the TV series generally follows the rule that one TV season equals one year in the storyline.
People in Westeros apparently just apply colloquial names to each hour of the day, i.e., the "hour of the wolf" is the darkest time in the middle of the night.
The earliest written histories date back to about 6,000 years ago, when the Andals first introduced writing to Westeros.
The First Men had no writing system more advanced than runes for marking graves, thus all history before 6,000 years ago relies on oral tradition.
While they seem to just refer to each month by number, keep in mind that this is essentially what the real-life Gregorian calendar does, inherited from the Romans, and their names often just stem from Latin numbers: "Sept-ember" is the seventh month, "Oct-ober" is the eighth month, etc.
Westeros also doesn't use an "o'clock" system of measuring hours in a day (they also don't have mechanical clocks).