I've heard that term tossed around my barn a few times, and I have come to understand it as a horse that has a stiff back/ does not use his back muscles properly. To have a good back, the muscles must be warm and flexible, so if the back muscles are cold they need a lot of warm up time because of stiffness. It can also be caused by an ill-fitting saddle or a bad riding position that blocks the muscles from moving properly, therefore making the back cold. By the way, dry spots usually mean a point of strong pressure, the dry area has been pinched. A particular spot of sweat also means pressure. When you take the saddle off after a good ride, the sweat dispersal should be close to even.
If you google cold back all of these things come up. the term was used by cowboys to destribe a horse that would buck when you first mounted him. After a few good pitches the horse settled down. I beleive was it really was was a poor fitting saddle that when the weight first settled on it and the back of the saddle dug into the loins the horse would hump it's back which actually filled in the bridge and helped releive the loins.
I know what you are saying about the sweat but looking at the bare tree, looking at it on the horse and then looking at the sweat marks it appears that the dry area was actually the area that was not touching.
In the wither area you actually get very little contact, only point contacting and my tree needed to be built up along the bottom edge by about 1/2 inch to make contact with his back.
All tree modifications are made with laid up fiberglass. Cloth and resin and yes areas were built up to 1/2 inch.
After I did the first tree and was satisfied with it I immediatley tore another new saddle apart and did the same to it.
I work on the tree during the day, take it to the barn at night, mark the area to be modified, back home for the day and back at night. Takes about a week to get it just right.
A saddle tree has only about 60 square inches of area IF it would all touch the horse. A 200 pound rider like me puts 3 plus pounds per square inch on the horse, way way too much.
My old browns saddle, my military saddle, both had over 300 inches of contact. A far better load spreading.
You don't walk in high heels over snow, no ,you use snow shoes to spread the load. A saddle is the same idea