I apologize in advance if the details I'm about to provide are too poor or distorted by my memory.
My father told me once of a short story which (if memory serves) is made up of the following plot: In the era of the wild west, some gang is attempting to rob a train. During the robbery, one of the heist men's horses suffered from a gunshot wound and was unable to continue. Once the gang was fleeing, the rider of the wounded horse asked the gang leader to double-ride with him. The leader looked around and said something along the lines of "the mare can't hold both of us", and rode on. I believe that so far the story was told from the viewpoint of the leader. After the events I described, he wakes up to find himself being a banker many years later (it was all a dream), sitting across a man who's trying to get some sort of loan approved. The banker thought, and finally replied "the mare can't hold both of us". Upon refusal, the customer killed himself.
Additionally, I'm pretty sure that the author was American (and rather known, probably wrote many short stories). Any help or leads would be much appreciated.