Taking your pony on the train
The keen pony book reader will know many books where a pony gets from A to B on a train. Rapide arrived at Jill's on a train in Jill Has Two Ponies, and Christabel Raffington's rescued Daybreak travels on a train in Josephine Pullein-Thompson's I Had Two Ponies. Train travelling horses were in fact legion, but I'm not sure if there's still such a thing as a horse car. From this story on BBC Wales, it would appear not.