@ossobuco,
yeh, Its usually a trailer for hauling your horsey. In the Chesapeake its also locally used to describe the sliding companionway hatch on the aft of a Bungie or a 7 log. (Itd be the Chessie equivalent of a "Booby Hatch".
On a deepwater sailboat of any kind, the name Booby hatch has a foggy etymology . Ws it where Albatross would try to stay out of the weather ? (That's one ). The term horsebox I guess comes from the shape of a horse trailer. kinda rounded up front, like the Booby hatch door
This is not anything of the Chesapeake , its a ketch named the Lorcha, out of SW Habah.
I could only find an example of a booby hatch and not a 'horsebox" , but they look basically the same