Actually, the American Saddlebred is spreading to other countries. The UK has a Saddlebred Association, as does Africa. I believe Austrailia does also, and I know there are Saddlebreds living there.
Africa actually has a very active Saddlebred breeding program and they produce some very nice horses, such as Arborlane Tango's Wee Pee, who was Fine Harness World's Grand Champion, IIRC, and is a very popular and respected sire.
I'd also like to note that Saddle Seat Equitation is open to any age amatuer, though classes are always divided by age. 18 & Over Equitation classes are very common at horse shows these days, and the National Championship Pleasure Horse Show has created a new Pleasure Equitation Olympics Division for Adult Riders. 2001 is the first year this class will be held.