Hi Will :) I never sold a horse abroad but I know that the vaccines need to be up to date and that a quarantine is compulsory in many countries. I know that in the US, a mare needs to be analyzed during 2 full weeks before being allowed to join their new stable.
In China, horses than are imported can't leave the country anymore (except some places in China if I remember well)!
I've bought my horse abroad and it wasn't complicated at all! The horse just needs to have its international papers up to date.
Depending on the country you live in and where you sell your horse, there might be a travail by plane, it's expensive I guess but nowadays it's quite easy with specializing companies, your horse just have to be in good health to handle the trip if it's a long one.