[Knight of Gondor]

Not possible. Absolutely inconceivable for there to be a train in Middle-Earth. I don't mean to sound unkind, but the answer comes as much from personal desire for there NOT to be a train in Middle-Earth as much as conviction that Tolkien was speaking from metaphor and not from actual comparison.

The whole fantasy/medieval nature of Lord of the Rings is what makes it worth the mental journey. It is a world so different from ours, with inspiring characters and thrilling stories. The lack of technology is what makes it such a romantic, fanciful and perhaps even idealistic world. The deep blast of a train-whistle would pull us back to the real world, not draw us further in.

It seems to me that the technology tree of Middle-Earth had only reached so far as siege weapons and initial dealings with gunpowder or other explosives. They were used in the fireworks, and had only begun to be weaponized by Saruman. (One might expect that cannons would not be terribly distant developments.)