I think Davos will march south with wildlings to reinforce Stannis. I mean, where else will the free folk go? The NW killed Jon because he brought them in. The NW will probably try to send them back beyond the wall, and instead many will probably flee with Davos

Davos doesn't know that Stannis is "dead". All he knows is that Mel abandoned Stanny before battle. He will do everything he can to get back to the Mannis.