There is no one size for a thoroughbred, you need to find the custom fit for your horse. To find out how to measure your horse for the saddle tree, see the related link.
I would do a close contact saddle or for western, a tree less saddle
A saddle tree is the frame on which a horse's saddle is fitted and built.
It sounds like you may have a 'youth' saddle. A pony saddle is pretty small and you would be able to tell right away that it was meant for ponies. A youth saddle is meant for that in-between stage when the rider has outgrown a pony saddle and is still to small for a full sized horse saddle. To find out you can measure the saddle's tree. Take a tape measure and start at the pommel and run the tape to the cantle. This will give you an idea of the size of the tree which is what the entire saddle is based on.
A treeless saddle
frame The hard part of a saddle is called a saddle tree.
The Billy Cook Pro Reiner 9602 appears to come in QH Bars, which means it is a wider tree size suitable for stock type horses.
No it is not safe to sit on a tree of a saddle stand if it is brand new or very old
tree
The tree
The saddle needs to fit BOTH horse and RIDER. Depending on the seat of the rider a typical pony saddle would have a 10 to 14 inch seat. You will need to have a longer girth on a smaller saddle.
This depends on two things - the width of the horse's withers and the femur length of the rider.The horse's withers determine the width of the saddle's tree. It is essential this fits well, as a bad fit may lead to sore, dry spots, and skin rashes, bucking, lameness, back pain and many other problems.The length of the femur (thigh bone) of the rider also determines the LENGTH of the tree of the saddle (pommel - cantle length). If this is too short, a rider will be positioned too far back - too long and there will be too much seat for the rider to fill.Saddle lengths between English and Western saddles can differ by 2 inches.It is best to have a saddle fitter our to determine the size of saddle you will need, that or visit a saddle shop.
wood tree