It is a horse that is uncomfy in its back, but does not have a bad back. my horse is only slightly cold backed and will dance on the spot when i get on, but was also very nervous when people were getting on her so she only likes one rider. Most cold backed horses will buck when ridden normally when taken into canter.
This is a basic answer, someone else might be able to explain it better.
Cold backed i would say is unhappy with thing on his back, saddles, riders or rugs... he will show agressive mannors in a way of saying "I'm not happy" Could be a bluff E.G a buck, kicking out, ears back, turning round and nipping etc or a more nervous looking reaction of tucking up and "humping" his back. It tends in my opion be from the bad breaking that happens were horses are not given time to understand and learn to be positive towards saddles. It could also be from bad experience like a badly fitted saddle/rug or rider. It can be treated be rebacking the horse to saddle slowly *Making sure it fits perfectly*
I would say a cold backed horse will be funny about getting on. They will often dip their back and once walked on will soon be normal. Have never know a cold back horse to buck into canter for that reason. I would expect it to only cause problems with mounting. It can be helped by careful mounting, allowing the horse 5 minutes between tacking up and getting on and sheepskin pads.
I have not heard the term cold back in regards to breaking at all - cold backed as far as I know it, is where the horses back requires warming up/stretching before it moves comfy! Every horses back needs to warm up, some just more than others. Some horses you can feel a hump in their back when you get on, which will settle with being light on their back, and taking your time to warm up and they will be fine! They say you can reduce the warm up time by putting a magentic run on them before working.
When I get on, sometimes he'll go "humpy" (his back will go up, with his bum tucked under) and dance about for about 20 seconds before relaxing and then he's fine (he only does it in the very initial walking away under saddle, he's fine going up into canter etc.). He's done it more often in colder weather. About 5/6 times he's really panicked and bolted and bucked til Ive fallen off. My boy is short backed though so I found it a hell of a job to find a saddle short enough in the seat to stop pressing on those ribs near the back (which makes them buck!).
It CAN obviously be due to a back problem but often people (like me) get their backs checked to no avail.
Some people say cold backed horses dont exsist, that its all in the horses head or the horses is just being naughty. I would disagree, my horse is not aggressive in any way - when he has got me off, its from genuine panic (he's a bit quirky). Apart from this, he is the nicest horse in the world.
there was a cold backed horse at the racing school, basically he didnt like too much pressure on his back, or pulling on it, so he was fine once you were on, but you had to have a leg up at a walk (Which was fun for little me on to a 16hh) and then you just had to walk for a few mins before making sure his girth was really tight.