Some big names, I don't know anything about them - other than they are big names. IRT - International transport of horses New Page 1 EquiAir Horse Shipping, International Flying and Equine Transport Professional Horse Shipping Company : International Horse Transportation : Horse Transport Services : Alex Nichols Agency
Fedex does it too, but I can't find a link.
More info, from here THE LOGISTICS
Generally speaking the options are a private charter flight or a commercial airline flight.
Charter airlines are generally contracted on an as-needed basis and are usually specially outfitted for that specific contract. Historically, charters are more common after a large sale with international buyers, such as race horses, or for special events such as the Olympics or large shows where a group of horses all going to the same destination can travel together at a reduced cost.
Commercial cargo shipping has become popular with airlines that contract with professional shipping agents. Because of the high volume of horses that travel commercially, we will focus mainly on that method of equine transport.
In the United States, the airports in Miami, New York and Los Angeles are used only for import. Houston (IAH) Chicago, JFK, Miami, and LA are most commonly used for exports, with DFW used occasionally.
What commercial airlines ship horses? El Al, CAL, Lufthansa, KLM, and Cargolux have the most livestock shipping volumes. FedEx and Emery transports also offer international equine shipping services.
The most common in-air transport vehicle, whether provided by the shipping agent or the airlines, is a special container known as an Airstable. Looking very similar to a horse trailer without wheels, one unit holds three horses and locks onto a standard shipping pallet. Some have movable side panels within the box to accommodate different size horses, or mares with foals.
The horses arrive at the airport via regular ground horse transportation such as a van or trailer. The airport will provide a quiet place to load horses into the Airstable. It is then moved by truck or tractor to the plane and moved into place in the cargo hold by cargo elevator and rollers on the floor of the plane. Some planes have the horse transport stalls built into the aircraft. Commercial flights may be restricted to certain airports, and they may be routed through a hub city, increasing the travel time substantially.
Once loaded, it’s not possible for the horses get out of the shipping boxes at all during the flight. According to one shipping agent, most flights are 6 to 10 hours, and rarely is a flight longer than 14 hours. The horses have room within the transport boxes to move a couple of steps back and forth and, as mentioned, some air boxes have adjustable panels. Most airlines do not take more than 6 containers, so 18 horses are usually the maximum head count allowed per flight. Weight as well as space is a factor in determining the cargo allowed. Equine Chronicle » Modern Pegasus – Horses Flying Internationally
I am not sure that this helps at all, but a while back I was looking at shipping a horse between American and the UK, the figures came back around $8k-$10k, just to give you a ballpark.