yes! You're right, there are societies for 'drum horses' though but they are not a breed x
In the UK we hardley ever use the 'paint' horse terms for coloured horses (like tobiano etc), unless we are refering to american paint horses that have been imported or bred here. Its Piebald for black and white horses and skewbald for brown (bay) and white or any other colour with white. This may be just the world of horses I have been brought up in though. I've never seen a paint horse in the UK although I know there is a stud stallion local to me that is a registered american paint.