@Light
Alot of these reasons could be answered with one factor: The Blood of the Dark Soul.
I'm Certain that no other painting in the history of souls could've ever been painted by the blood of the dark souls or any particularly special/ powerful soul, its not like Ariamas was made from gywns soul or anything.
Ariandel used blood to extinguish the flames, in the painted world of ash.. a world made from blood.. there was no fire to begin with, thus something like rot never became a factor.
Who knows what differences the blood of the dark soul made with its power compared to other paintings?
Considering the painting itself is literally just blood, its believable that the blood is the counterpart or connected to flame.
About it being dark forever? Besides the ending when have you ever seen a light day in bloodborne? Not to mentiom since, again, the world is litterally made out of the blood of the dark soul, which came from the first flame, its not impossible for the night of the hunt to be related to the age of dark, either through the world of dark souls and bloodborne co-existing; that the painted world of ash is just hidden/ mostly destoyed and the regular world of dark souls still lives on continuing its cycle, even a scrap of the painting could still contain the entire world, like Ariandel.
Or even the hunter can end the night in their painting in a similar fashion to how one linked the fire, when choosing the ending where gerhman kills you and light is revealed (only in that ending) its likely to have had something to do with the hunters dream ending, of which the moon presence dwells, Its called Moon presence for a reason right, I'm definitely not certain.
The 'Cold and Dark' Aspect is likely just created from the original painters image, simply they painted an icy landspace, a icy landscape appeared, its completely unknown what was painted on canvas for the dark soul's blood.
As for time and dreams? The only theory I have on such things is that time could move much faster in bloodborne, following my previous points (Dark souls and bloodborne co-existing, the age of dark being the night of the hunt.) An entire age of dark in dark souls is but a long night in bloodborne, this could also mean that dark souls is still partly medival and bloodborne is advanced. It's just speculation so I have no idea, I can't really say anything on dreams either.
As for hollowing, again I'm not certain, I mentioned in my previous comment very few or no people 'escaped' into the painted world and it's possible for living beings to have been made inside the painting with no contact or knowledge of the outer world, thus having nothing to do with hollowing or the dark sygil, being such as the great ones we're likely birthed from the painting.
Plus y'know.. moonlight greatsword.. and patches..
But in conclusion we simply can't know, its dark souls what could you expect? '\._./'
Im not saying you or anyone is wrong these are just my opinions for something I love to believe in.
I mean.. the night of the hunt = age of dark is a pretty cool theory right?