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One of the wildlings has 5 in the ACOK start.
 
Followers of the Old Gods, Beyond the Wall Old Gods, members of House Farwynd and Westford have a chance of the event chain firing for their children. It will start with the message that your child is having Green Dreams, from their depending on how the guardian reacts to it, they can either have nothing mroe happen, become a green dreamer like Jojen or become a potential skinchanger. A child who is a potential skinchanger will then have a chance of obtaining an animal companion within a few years.
The AI is weighted in such a way that Northerners will predominantly choose the path that leads to green dreamer and Wildlings will predominantly choose the path that leads to skinchanger.

The event chain is rare 100 years without seeing it is not strange, however it is much more common for Beyond the Wall Old Gods followers (Wildlings)
 
So for exemple a Lannister have no chance to have an animal ?

Or a lord pirate to have a whale ? ^^

A pirate? No, because being a pirate is based on having the pirate religion.

A Lanister? Yes, only if they are a follower of Old Gods or Beyond the Wall Old Gods.
 
Too bad. I'd like have a animal with a character in the south. Thanks

Certain things are religious specific flavour. It's the same reason that followers of the Seven can't get a Red Priest to use a Shadowbaby or followers of the Old Gods cannot become Knights.
Skinchanging and greenseeing are intimately conected to the Old Gods.
 
If you really want to use the console to enact the events that gives people animals, do so. I did it for one of my games (as well as giving my liege the King a dragon and my character greendreams, as well as making Children appear south of the wall and a bunch of other crazy things to happen... it was my way of bringing magic back to the world). Twas fun.