Originally Posted by
ducklord
It's probably best not to think about it too much, either from a character or a reader perspective, 'cause that way lies madness.
That said, here's my take:
For the overwhelming majority of characters in the DCU, reality, history, and their memories make sense. If you asked, say, Captain Cold to give you an overview of his life story (presumably after buying him a beer or two), he would rattle of the details of his childhood, his origin, his fights with Barry and Wally, his dalliance as a member of the JLA, perhaps, and it would all be a coherent through line. At no point would he say something like "and there was a version of me that gained ice powers for a while, but that never happened now." History, whatever it actually is currently in the DCU, exists. If you're a civilian in the DCU, you can look it up on Wikipedia.
A small minority of characters in the DCU are aware that their history has been over-written several times. Mostly, these are big-time super-heroes (since their histories tend to get re-written a lot), but it also applies to some villains. Sometimes they get flashes of their alternate lives at the writer's convenience. But since, as I said, that way lies madness (I mean seriously, how messed up would YOU be if visions of your alternate continuities kept popping up in your head?), it's not touched on very often except in the name of fan service.
An even smaller number of DCU characters are aware of the specifics of previous continuities and histories that have come together to forge the current timeline. Mostly, these are the cosmic god tier characters like, say, Darkseid and the Guardians, but Wonder Woman and Superman in particular are likely carrying around a lot of specific knowledge about the pig lips that have been ground together to make the sausage of the Infinite Frontier DCU.
This "it all happened, it all counts" is great for explaining why a forgotten and retconned away story may suddenly slip back into canon at a writer's whim, but that doesn't mean that contradictory stories are simultaneously true in the DCU. 'Cause again, that'd be madness.