a song of ice and fire - Why we have no (or close to none) children of the forest in the north but beyond the wall

Alright my history and geography on Westeros might be a little shaky so feel free to correct me on any presumptions

So , Westeros was covered with the children of the forest from the north to Dorne before the First Men came .

After the first man set their foot on Westeros there was a big war between them and the children of the forest which lasted for centuries if not decades.Finally there was a truce and Westeros was split between the first man and children of the forest .

As per the truce, the children got the deep forest and the first man the rest...now we are to believe that henceforth the children dwell in the forest INCLUDING THE FOREST OF THE NORTH ..... until the Andals came in.

With the ships of the Andals landing on Westeros several years after the truce ,the Andals burned and ravaged the deep forest settlements of the children and pushed them north. Thus decimating the population of the children.

My question is if the Andals were solely responsible for desolating the children of the forest in the south and pushing them north why is it we don't find any Children of the forest in the north where they can't be hurt by the Andals and would be protected by the truce (between them and the first men)

The books however tells us that the only place the children live now(found at) is beyond the wall(at least for sure ),

I understand and accept the children of the forest being driven to extinction anywhere but the north .

Well I know that truces can be forgotten and the first men could start killing the children again but I highly doubt this as the north is big and thus the first men should not have any reason NOT to share it the children and breaking the truce(considering they remenber and hold honor high).Also they now share the same religion as the children so cultural hatred would be dampened as well.

And even in the case of north-men eradicating the remaining children in the north why is there no mention of this in history as by this time the Maesters were a thing in Westeros.