I can speak to the issue of hardening & case hardening just about anything made of steel.
Been doing it for years on pocket knives, flintlocks, revolvers, tomahawks, hand tools, dental instruments...whatever.
Fotos show a repro 1851 I picked up at a gun show circa. 1996. It had a factory mistake on it and must've found it's way into the flea market when someone discovered it.
I annealed the main frame & internals, fixed the mistake, made some replacement parts, carburized all the internals, main frame, cylinder, loading lever & ram, and left the barrel alone.
Then hardened & tempered all the carburized parts, including the cylinder: each part tempered for it's application.
Some of the colors are different looking, 'cuz they're tempering colors. Wasn't interested in case hardened beauty. I want wear resistance. Especially on the cylinder. It was so soft, from the factory, that the cylinder locking bolt would've torn it up in no time. The cylinder doesn't need to be stronger. It's prolly stronger in the elastic annealed/normalized state. Hardening to much brittles it up & makes it more likely to grenade. Case hardening keeps some of the internal elasticity while making the surface wear resistant, as already pointed out.
My process is pack carburizing w/my own almond wood charcoal, sodium carbonate, & thinned asphalt to bind them together, inside a welded up square tubing steel pot I can wire down a top on. It's very aggressive. Can diffuse a case depth of .035'' in 2.5 hrs. at 1600'F.
Barrels, on anything that goes bang, are never hardened/heat treated to my knowledge. Barrels are made from stress relieved ordnance steel. Mainly so they won't warp when machined, ie. bored, reamed, rifled, contoured...etc. Alota muzzleloading rifle barrels are made from 12L14. It's about the softest steel ya can get. Machines beautifully. Good elasticity. Very stable.
I guess hammer forged barrels must have some work-hardening effect in them.
Pulling a rifling button thru a barrel prolly work-hardens the bore surface a wee bit. Which is why bench rest shooters leave their barrels billet diameter.
Cut rifling would not.
But heat treating a finished barrel ruins it's stability. Heat treating, for improved hardness & wear resistance, puts stress into the steel. Temperature changes in stressed barrel steel makes a gun shoot around corners. :-D A cylinder is so short, that any such effects are negligible.
However, case hardening my cylinder made the cylinder pivot hole reduce in I.D. I had to make a lap to restore it's I.D., to get it back on the pin.
OK. Don't mean to sound like a knowitall. Hope you can use any of this stuff.
Let me know if I can be of help.
Doak