I'm just at the end of reading The Goblet of Fire to dd and have noticed that when the carriages come to collect them to take them back to the Hogwarts Express they are referred to as 'horseless carriages' and there's no mention of Harry being able to see the thestrals.
I haven't read The Order of the Phoenix for a couple of years but doesn't Luna tell Harry he can see the thestrals because he witnessed Cedric being killed?