I think that there is zero chance that Jon is gone from the story. IMO it's just a matter of how Jon's character goes forward. Possibilities include
Jon warging into Ghost and his body dying. We know from the Varamyr chapter though that if that happens, Jon will ultimately "disappear". Someone else, perhaps Sansa, could warg into Ghost, but it still would mean the end of Jon.
Jon could be gravely, but not mortally, wounded. This scenario is problematic because of the chaos that must ensue after Bowen Marsh stabs him, and what would happen to his body, who would bring it to safety, etc.
Jon could die and be resurrected by Melisandr. Not impossible, and certainly the groundwork has been laid for this happening. it would also satisfy some people thinking that this event would satisfy the Azor Ahai reborn prophecy, although I believe that the prophecy doesn't mean dying and coming back but rather, someone who was born after the original AA died who will become AA, no death required.
Jon wargs into Wun Wun. I don't think that would work out too well. Wun Wun trying to fight off Jon's invasion might actually bring down the Wall
The most likely scenario IMO is the one Needle fine tuned and finished- The bodies in the ice cells were there for Jon to "practice" with. Dead bodies won't fight off a warging invader. The body that Jon is now inhabiting is glamoured by Melisandre to LOOK like Jon. The body that Jon is controlling gets stabbed to "death" by Bowen Marsh, but Jon's actual body is safe (somewhere, maybe in the ice cell, hence "only the cold"). Jon is alive, unharmed, and free to do whatever.