The last glacial period ended in about 10,000 BC, which is very ancient in historical terms, but considerably younger than still-existing Australian Aboriginal cultures, for example. Do we know of any ancient legends, folk tales, motifs, etc, that can be reasonably associated with knowledge of an ice sheet in an area where there is currently none?
This is a report that describes an analysis of indigenous Australian oral tradition that may (emphasizing MAY) refer to rising sea levels at the end of the most recent glaciation. It is an interesting approach that exploits a unique situation: because aboriginal culture remained in Australia unaffected by outside influences for so long, it is possible to look for these sorts of long-term cultural memories.
It is much more problematic to seek this sort of insight in cultures that are more "churned up" by the movement of people and oral tradition. I know of no analysis of European folklore along this line - certainly nothing that can be regarded as credible.
There was a similar post a while back with some really good answers in r/askhistorians. https://www.reddit.com/r/AskHistorians/comments/3lsmw1/whats_the_farthest_back_in_time_an_oral_history/. (There were no answers relating to ice sheets, however, there were some good examples of cultural memories going back 10,000+ years)
I'm a geologist/paleontologist not an historian, but I think I have something relevant to share.
Where I live the local native people, the Mi'kmaq, have a legend of their god, Glooscap, getting angry at a beaver for making a giant dam. Glooscap smashed the dam, and the Bay of Fundy flooded in.
Spicer, Stanley T. (1991) Glooscap Legends. Hantsport, Nova Scotia: Lancelot Press.
This is just one of the many legends around here, but quite interestingly recent geophysical data, spurred by ongoing interest to harness the bay's tidal energy, has unearthed (hehe) several distinct glacial formations in the bay (long flooded over), including a rather large terminal moraine. That's a big pile of gravel and clay pushed by a glacier, and they can dam things up quite well.
It would have been present long after the Laurentide glacier retreated and the Mi'kmaq likely would have noticed it (they have some deliciously detailed stories that tie into geological phenomena!). It may have broken as sea level rose, and, if so, that would have been a spectacular flooding event.
There was an interesting assertion that was quickly deleted, but which nevertheless warrants comment, namely that since the Australian Aborigines were some of the first people to leave Africa, they would, perhaps have the longest cultural memories and could therefore recall events from the most recent glaciation.
It may be obvious, but let's remember that everyone today is a descendant of people from whatever period in the past one is considering. The Australians are not unique because they have non-African roots that reach further back (we all have roots that reach far back). They are distinct because they arrived on their large island, became isolated, and apparently found little inspiration to change their culture.
What I suspect is really being asked here is whether there are any European motifs in its collective folklore that recall the ice sheet and its melting. Elsewhere, I provided a generic answer that this was not likely. But let's drill down for a moment, since people are people whether they are in Australia or Northern Europe: so why might we suspect these recollections in the oral tradition might be preserved in the former but not be surprised that they no longer exist in the latter?
As indicated, elsewhere there was a whole lot of movement of people and cultures in Europe, causing the stew to be constantly churned in a way that apparently did not happen as much in Australia. If there was cultural tenacity in Northern Europe, we might expect a recollection of Doggerland, for example - referring to the North Sea land that was once apparently inhabited but which flooded during the gradual rise in sea levels at the end of the glaciation. Why didn't Europeans recall this in their pre-industrial folklore? The answer is not entirely clear, but I suspect that it has a lot to do with how Northern Europeans were often on the move, that they lost touch with the earlier culture that retreated to high ground and asked themselves, "what was all that about?" Those people were washed offer by repeated influxes of other people, languages, and cultures. Their DNA may persist in part (together with that of a lot of other people who generously shared their genetic information), but DNA does not equal language, culture, or folklore. Change has been a dominant factor in the European experience, and although one should not ignore cultural continuity (since there is always a fair amount of that also), change is not conducive to long cultural memories.
Related question: do we know if the last glacial period inspired aspects of the mythical Norse frost giants?
This question makes me intrigued in the whole idea of "cultural memories". What is the oldest such "memory" that we have preserved?
Do we have any stories of true events that are shared between multiple distant cultures?
The only thing I can think of right now is accounts of things like the solar eclipse of 1185, mentioned in The Tale of Igor's Campaign, and possibly in Welsh Chronicle of the Princes.
I'm curious as to what the oldest such "memory" that we have is, though.