On her way to Winterfell, Arya stops to rest and make a fire. As she is warming herself by the fire she suddenly finds herself surrounded by a pack of wolves. One of those wolves, who is much larger than the rest, is Nymeria.
Arya asks Nymeria to go home with her but Nymeria retreats to stay with the rest of wolves. It is possible that Nymeria senses the violence instilled by Arya and wants to have a more peaceful life with the wolves. Whatever the reason, it is clear that Nymeria no longer needs Arya and will not be going with her to Winterfell. I think it is possible Nymeria will return to Arya at some point.
