Obviously it is good to check the physical stuff, although it sounds like you are on top of this. On the other hand, horses can get cold-backed in the winter and it’s really just that and nothing else. Warming up the muscles properly and well can sometimes take longer than we might think.
A friend’s winter-time tight-backed mare always benefited from her Back on Track quarter sheet thing; she had a long one and a shorter one and used them as the saddle pad itself. There was a marked difference for her if she just used a regular pad. My friend also sometimes just got on and did stretchy trot from the get go. This seemed to unstick the back and once the mare had snorted a few times, she went back to walk and started her ride from there.
My old man, before I retired him, started his rides with his nose on the ground. Bigger and bigger steps, long and low, until he was swinging and very free in his back. He was off the track and nearly always needed a huge amount of this type of stretching before we could ask him for even mild lateral or any collected work. Sometimes he just needed a few laps of canter before anything else, but that’s an OTTB thing, I think!
Even my jumper, who is a stereotypical WB and has about as much sensitivity in him as a grapefruit, can get cold-backed in the winter. While I’m grooming I throw his BoT sheet on, give him a fat flake of alfalfa to munch on, and I use a square pad lined with sheepskin as my saddle pad all winter. He dislikes quarter sheets, but when it’s really cold I use one and this seems to help.