trumpet bells can be made of a variety of materials and the metal alloy chosen directly affects the sound ... cryo treatment changes the metal, vaguely akin to tempering.
If tempering were desirable, why don't the trumpet makers simply temper the metal? Or use a stiffer type of metal? And why cryo? They could just temper it or choose an appropriate stiffness and be done with it, no?
Some do indeed temper their bells. The problem is that it's not necessarily "desireable". As with audio, there's plenty of disagreement.
Just so you know, bells are available in a wide range of materials, from sterling silver, to cheap yellow brass, with all types of steps in between with various copper and nickle contents. Some are annealed and some are not, some have two or three combinations of metals, all of which influence the sound, before you even get to the most critical element, the shape of the bell flare itself, which must be in appropriate proportion to the leadpipe taper, etc.
The number of choices available are pretty stunning, but it's interesting to note that most of the orchestral pros pretty much stick to about a handful of makes and models. When I tell Elk that my Bb is a gold plated 1960 B1, he knows exactly what I play and even will surmise a little about my personality and probably be correct.
Anyway, the effects of annealing and cryo on sound are actually not agreed upon. Despite that, makers provide these choices and trumpeters battle on online forums about which is "best." Sound familiar???