Symbolism, Imagery, Allegory
If you noticed the pony and trap recurring and thought, "gee, anything that shows up so often just has to be a symbol," well, you'd be right. For Arthur, the pony and trap are a flashback to the past. He arrives expecting a car, but:
No car appeared. Instead there drew up outside the Gifford Arms a rather worn and shabby pony and trap. (5.1)
For Arthur, this goofy mode of transportation represents an old-school England in which cars and trains are not relevant and everyone travels in carriages and on ponies. It lets him think that the villagers are just a bunch of hicks who probably go muddin' and cow-tipping—and he might be right about that. But the pony and trap also comes to represent a lot more.
Specifically, it represents being stuck in the past. When he comes to Eel Marsh House, he begins hearing the sounds of the pony and trap on the causeway, but it's not a cheerful trotting sound:
It had somehow lost the causeway path and had fallen into the marshes and was being dragged under by the quicksand and the pull of the incoming tide. (6.6)
He hears this again and again…