I've been a knife maker for many years, and have experimented with cryogenic treatments. On stainless and some exotic alloys, they may have significant benefits. On common tool steels, not so much. A rifle barrel is not an extremely high carbon steel, but is certainly hard enough for it's purpose.
To harden steel, it is heated, and quickly cooled. This gives great hardness, but is not a desireable form of the steel. To be useful, it must also be tempered. This is what creates desireable metal for tool use, and I would guess, for gun barrel use. A measure of manganese in the alloy would give it wearability.
If the metal were heated to non-magnetic state, (about 1500 degrees F.), then cryogenically cooled, it would be very hard, very brittle, and very STRESSED.
If the same mild steel were tempered in an ordinary fashion, in a tempering oven or such like, it would make a machinable, mallable workable steel with long life properties.
IMHO normal heat treating will suffice for the type of steel in a gun barrel.
When steel is heated quickly, it will respond to the heat by expanding, then contorting. The movement can be observed by laying a bar on a steel table, marking along side it, and applying heat with a torch.
Stainless steel is less subject to the movement, but has other factors that might affect it in a gun barrel.
Just thinking out loud......Most of what I know I learned making tools and knives, not guns so I'm probably way off base........
Ben