Hey new posted, so don't be too rough on me.
I've recently been trawling my way through the GoT and the whole Bran/Children of the Forrest story line has really interested me.
So I've been doing a bit of research on Coldhands, and I came up to a few interesting lines..
As a preface, I personally believe that he must be a member of the nights watch as most people seem to share.
"They killed him long ago" makes me believe that Coldhands cannot be Benjen Stark, as the Children of the Forrest live for so long, "a long time ago" must be longer than the two years ago when Benjen went missing/died.
I think it was Brandon Stark the thirteenth Commander of the Nights Watch.
Now when I did some reading into Old Nans tales, , the thirteenth commander of the nights watch who was erased from history because of his relationship with a woman who is described to be essentially one of the Others "her skin was as cold as ice". She also alludes to the fact that he was a Stark and shared the same name as Bran.
That would one solve the problem of Coldhands becoming a wight (due to his relationship with one of the others) as well as coldhands being dead for some time, as this was during the age of heroes.
But also when Coldhands responds to Bran's question about his history, he replied with "Your monster, Brandon Stark".
Now what happens when instead stating that he the monster of the living Brandon Stark, he is instead stating the name of the living Brandon Stark's monster is Brandon Stark?
So what I'm getting at is that because the thirteenth commander of the Nights Watch is probably called Brandon Stark, and that the current character is called Brandon Stark, the meanings of this sentence could easily be confused.
This could also explain why he could not travel under the wall, but had knowledge of the black gate. He was cursed and effectively an oath breaker in terms of the Nights Watch