I unfortunately never watched the movie myself, but I remember reading about it in an article about 4-5 years ago, which had a decent amount of details. It was an older horror movie, considered to be one of the first "slasher" films. The action is set in the house of a mountain-climber (I want to say specifically called out as having hiked Everest) who is, I think, a former war veteran (possibly of one of the World Wars). Early in the film, he turns up dead, I think decapitated. Not long afterwards, people in the house start dying, killed someone wielding an ice axe formerly belonging to the climber.
Ultimately, it's revealed that the killer is indeed the climber, with it initially seeming that he faked his own death, and is killing out of some sort of war-induced PTSD, but near the end of the film, it's revealed that he actually did die, and it's his ghost killing the people.
I recently (somewhere in June-July 2019) came upon a modern film with a similar plot, down to it being an ice axe used in the killings, and thought I could track down the film to comment on the plot getting ripped off, but I couldn't find it at the time. I've since forgotten where I saw the mention of the modern film, or what its name was.