It appears that they were flown...and to Hong Kong (not Beijing)....
Copied and pasted from an
article:
All the horses attending the Olympic and Paralympic Games will depart form five hubs around the world, chosen and approved by the Organiser. These are: Amsterdam, London Stansted, New York, Los Angeles and Sydney.
Horses will travel in 'Jet Stalls" with two horses per stall. Flight times vary between 12 and 15 hours with some aircrafts stopping at Dubai en route. The temperature in the aircraft will be 17 C approximately.
A Peden-appointed professional groom will accompany horse attendants on the flight, and attendants will travel through security with their charges in the 'Jet Stalls'. It is expected that horses will be in their stables within 1 hour 50 minutes of arrival in Hong Kong.
Ruthie