This is an area of high controversy and horse people have wildly differing opinions. I wait until at least 5 years old. The larger the horse, this will extend to 6 years old.
It is wise to wait until the growth plates have finished fusing. The vertebrae are the last part of the skeleton to fuse and this is not complete until 5-7 years (longer for larger horses). There is a lot of weight on a horse when they're being ridden and this can cause problems with the spine, such as kissing spine.
Waiting is not a bad thing, it gives the horse and owner plenty of time to establish a relationship and have solid groundwork. It's preferable to have the horse completely comfortable with everything you're asking on the ground before asking for it from the back. In my view, it's always the horse's best interest that comes over the human. So if it's better for the horse physically to wait, then I recommend waiting.
You're obviously keen, if you can possibly hold off for another 12 months until she's nearly 4 (not rising 4) it will be beneficial for her. Bum high is an indicator that she is still growing. She is not that big, and 14 stone is a noticeable weight. I know a trainer who is tiny at 50 kg (7.5 stone), when she hops on a horse there is less chance of strain. The plus side of being 14 3 is that she will probably be finished growing by 5 yo.
Riding too soon can cause the horse stress and strain in the back. If you horse is in pain, this will present itself while riding or even just saddling. So it is wise to hasten slowly with horses. As Rick Gore (horseman) says - and this is a messy paraphrase - there's a long way to do things and a short way and the long way is always shorter. Or with horses there's an easier way and a harder way - the harder way is usually the right way. Taking the time to put in that extra effort and patience yields results that outweigh the wait.
So this is probably not the answer you want to hear, and ultimately it's your choice. With horses, there's so many opinions and many people will disagree with mine, but that's all I have to offer with my experience, research and what I do with my own horses.
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Not sure where this image originated
Damage to the soft tissues is the most common cause of back soreness in the horse. This mostly involves the group of muscles along the back. Usually, all or parts of these muscles are strained while the horse is being ridden. The principal sites of damage are located just in front of and behind the saddle area. Signs include alteration of the horse’s performance and acute back pain. Most of these injuries respond to rest and physiotherapy, although several weeks may be needed for full recovery (see also Muscle Disorders in Horses).
Another fairly common site of soft-tissue damage is the ligament that runs down the middle of the back. Signs of damage to this ligament typically persist longer, and the chances of complete recovery are not as good as for the uncomplicated muscle strains.
There is considerable controversy over the diagnosis and treatment of back problems in horses. Much credit is given to the value of physiotherapy, particularly chiropractic and osteopathic manipulation, but there is often little to substantiate their effectiveness.
The spinous processes are the bony structures that protrude upwards from the body of vertebrae. You can feel their upper points in the midline of the back between the large back muscles. They do not normally touch each other; however, with kissing spines syndrome, 2 or more do. This may be partially due to the effects of bearing a rider. When this occurs beneath the saddle area, some horses develop back pain. The condition may also cause a local bone reaction, small bone cysts, and false joint formation. Diagnosis can be aided by injection of local anesthetic into the affected spaces between the spinous processes. Many cases respond to rest and physiotherapy, but persistent cases may require surgically removing one or more of the tops of the spinous processes to relieve the crowding of the spines.
