The pine trees themselves can be seen as a haunted element. In many cultures, pine forests are considered spooky places. And in the story, perhaps the pine trees witnessed a tragic event like a murder or a sudden death, which gives them a haunted quality.
Well, the lyrics often mention things like a 'long black train' which can be a symbol of death or something ominous. In the context of the true story behind 'In the Pines', this could be related to an event like a mining accident (common in areas with pine forests) where many lives were lost. The train could be taking the souls away, and that idea of the afterlife and the loss associated with it is a very haunted element of the supposed true story.