Our chronological resolution is not really good enough for this for the start of the last Ice Age (Glacial), about 110000 years ago. To establish whether it is noticeable within a lifetime or so, you need a time resolution of the scale of decades, or 0,01%. That is a bit too much for marine isotope cores, our main proxy for climatic data this far back. However, at the beginning of the current inter-glacial (14000 years ago or so) we have ice-core data, which is much more precise. From these, we are able to reconstruct (supported by a number of other proxies, such as pollen and lake cores) climatic changes on a much finer scale. A major cooling event like the Younger Dryas, about 12000 years ago, seems to have taken place withing a few years and definitely within a human lifetime. A cooling event like this was enough to bring back glaciation in England, for example, and the climatic shock effect in the Near East might have been a primary catalyst for the start of agriculture. Similarly, a later climatic event at 8200 years ago brought about many changes in Near Eastern ways of life, suggesting also that this event would have been noticeable and abrupt, rather than slow and gradual. While we do not know the myths and legends, or oral histories, of the people back then, it is quite likely that these kind of events would have been remembered and known.