Update: Unexpectedly, I can now answer my own question - a few minutes ago, I was looking at secondhand Playmobil adverts, and much to my surprise, I found this item for sale! It's a 4316 Horse Cargo, part of the airport series.
So I was wrong about a horse NOT fitting in it - I obviously tried the wrong horse.
The missing door turns out to be a 'wooden' ramp .... which I already had in my 'Unidentified Objects' box. Guess I just need an airport to go with it now......