It's a horse that doesn't like it if a saddle/rug/rider is placed on their back. (Mine objects a bit to a cold rug actually!) Some of them buck and bronc and some have to be ridden in a forward seat until they've settled. The thing is that a cold-backed horse can be exhibiting symptoms for all sorts of things, back problems, kissing spines, liver problems etc, and may not just be cold backed at all. I guess that is the conclusion some people come to when everything else has been ruled out.