As much as I love horses, I wouldn't be too happy with a horse on a train. They are much too easily frightened, with sudden movements and loud sounds often startling them, which may result in bucking, rearing, etc. Obviously, if a horse were to get spooked on a train, both the horse and the passengers would be put at risk, not to mention the potential damage caused onboard the train.
I can just picture some small child running down an aisle on a train, spooking a horse. As much as the parents should be controlling their child, situations like this would be incredibly dangerous. Recently, as I was leading a horse in, a pony came cantering down the hill, and my horse went absolutely crazy and wouldn't stop kicking! Thank God we were in the field at the time - if in an enclosed space, the outcome would have been very different...
Although, I did read somewhere that they were training a miniature horse as a guide animal on the Tyne and Wear Metro. If I ever needed some sort of assistance animal, I'd certainly opt for a horse or pony if the option were available - never been a fan of dogs, particularly on trains, if I'm honest.
Edit: Here it is.
https://www.google.co.uk/amp/s/metr...rides-train-prepares-life-london-9257621/amp/