In an essay I am writing, is it incorrect for me to say The stables housed over a thousand horses, or should I say The stables housed more than a thousand horses?
While 'more than' may have been the correct answer in the past, 'more than' and 'over' are now considered interchangeable in relation to numerical values.
From the Grammarly Blog:
According to the AP Stylebook, “more than” and “over” can now be used interchangeably to indicate greater numerical value, and “less than” and “under” can be used interchangeably to indicate lesser numerical value. Prior to the rule change, the only acceptable use of “over” was as a locative...
("Synonymizing 'More Than' and 'Over'", by Allison Vannest)
The two sentences mean more or less exactly the same thing. Your choice between them is a matter of taste. If the exact number of horses was 1012, say, I might slightly prefer "over", whereas if the number of horses was much more than 1000, maybe 2000, my preference would be for "more than" which is, perhaps, a slightly vaguer term. But it is quite possible that another person would read the words in the opposite way.
So my conclusion is that unless there is some very specific additional point about the number of horses bot are quite correct.