I have this theory that I've been excited to tell someone about.
"Coldhands" who bran and co meet and helps them on their journey... that must be benjen stark isn't it?!!!
I have this theory that benjen stark, being mortal, succumbed to the blue eyes affliction of snow zombie (whatever they are) like the others, however because he's a stark, the blood of the first men flows through him and his stark blood allows him to retain his memories and control of his faculties.
So because he's only human he still turns into one, but because he's a stark he still remembers who he is and who bran is when he refers to him by name and isn't completely full snow zombie