A horse that is 'cold backed' is one that will buck, usually when they are fresh, right after they are saddled. They are similar to a 'cinchy' horse and many 'bronchy' horses are both.
The horses that have tender skin and/or sore backs are horses that will literally 'scrunch' down to avoid even a soft brush or light hand being run over their backs. They will drop down 6 inches to get away from brushing or rubbing their backs.
The one that made a believer out of me (about 20 years ago) was a big, gray, beautiful OTTB that I bought at an auction. He took short, mincy steps and would not even come close to stepping in his front tracks with his back feet at either a walk or a trot. He showed no lameness or was not 'off' in any front or hind foot. He just did not travel very well.
The other thing I found out was that you could not even brush this horse without him scrunching and scooching down and away from even a soft brush. I ended up having to softly bathe him very carefully to clean him up for saddling. He even scrunched down from the water hitting him. He had the most tender skin I had ever seen. Even his shoulders could not be brushed.
I had seen race horses that were diagnosed as 'body sore' and the Vets diagnosed 'turn-out' for them. He was worse than any of them.
What was really baffling was that there were several race track 'wins' listed on the back of his papers. He had run successfully, 'cheap' (all cheap claiming races), but wins just the same. He did not win them with his little short, mincing stride -- even cheap races.
I took him to the Chiropractor in Weatherford, Texas. He walked into his barn with his hind feet missing his front track by 8+ inches. He walked out of the barn over-reaching his front track by a foot, after one Chiropractor visit that took less than a hour. Even more amazing, I could brush him as hard as any other horse. ALL of the tender skin and sore back was gone, for good.
I paid $900.00 for him at the auction and 6 months later, well started over fences, I sold him for $15,000.00 and he made a high level hunter a year later.
I bought him at the auction from someone that had taken him from the track and tried to do the same thing, only they gave up on him because he was a poor mover and always had a sore back no matter what they did with saddle fit, special pads, medications, etc. One Chiropractor visit to a GOOD Chiropractor was all it took.