Howdy
I think it is a very interesting question too. I am very interested in the materials used in early mass produced guns.
It is true that a lot of early guns used iron instead of steel. I have a fabulous video made about 40 years ago of Wallace Gusler, the gunsmith at Colonial Williamsburg, making a flintlock rifle from scratch. He is duplicating the methods used to make a rifle in the 1700s. He plainly states that he is using iron, not steel for the barrel and all the parts of the lock. The only steel he uses is some spring steel for the springs.
Despite the fact that the Bessemer process was discovered about 1851 and patented by Bessemer in 1855, malleable iron was still being used for firearms production much later in the 19th Century. Most notably, according to Kuhnhausen, the Colt Single Action Army had cylinders and frames made of 'materials generally resembling high grade malleable iron' up until about serial number 96,000, which would have been in mid 1883.
I suspect, it might not have been so much when the material was available, as much as when there was a method available to economically make gun barrels from steel. And this hinged on when the gun drill was invented. The method that I have seen most commonly used for making rifle barrels from iron was a roll forming process. This is what Gusler used. He basically took a long bar of iron and hammered it into a flat strip called a skelp. Then he heated it again and slowly wrapped the skelp around a mandrel, welding it together with one long weld the length of the barrel into a tube. This is not the same as the Damascus or twist steel process, where the barrel is made up of many welds in a helical pattern. With a rolled barrel, there is simply one long weld the length of the barrel. The bore was then brought to final dimension with reamers, and the rifling done by hand with a manual rifling machine. All of this was of course extremely laborious and therefor expensive. The outside features of the barrel were formed by filing.
By the way, barrels made by this process could be very fine barrels indeed. They were capable of excellent accuracy, only limited by the skill of the gunsmith. With soft lead and Black Powder, their wear qualities would be fine and they would last for many years. It was only the coming of Smokeless Powder and the attendant higher pressures that necessitated barrels be made of steel. That's why Colt did not factory warranty the SAA for Smokeless powder until 1900, the steel they were using was no capable of withstanding the pressure until that date.
I have seen diagrams of mass production equipment using the same principal, where red hot strips of iron would be run through progressive rollers, each one cupping the strip a bit more until a tube was produced. The barrel would then be welded 'shut' with one continuous weld.
All this was done because there was no way to drill a long straight hole. When the gun drill was invented, very deep, straight holes were possible. A gun drill has one or more holes running the length of it. Coolant is forced through the hole, providing coolant at the cutting surface and providing a way to clear chips away without clogging the drill.
Unfortunately I have not yet found a reference to exactly when gun drills were invented. But modern steel barrels would have been impossible to make without them. It could be that like so many other 19th Century inventions, the gun drill was invented right about the time when the Henry rifle was being developed, making quality steel barrels possible. Just a guess, I really would like to know when the gun drill was invented, but so far I have not been able to narrow it down.
I found the paragraph in question in the Sword book, and I believe that Oliver Winchester knew the difference between iron and steel. The reference is to a letter he wrote in 1863 complaining about the Liverpool firm of English and Atwater and their failure to deliver '500 steel barrels'. So I suspect if he wrote about steel barrels, he really meant steel barrels.
As to why was Winchester importing steel barrels, I think it has more to do with the manufacturing capabilities of his own factory. When Winchester took the helm at the New Haven Repeating Arms company, the place was very low on cash. They had had some unprofitable ventures that had sorely depleted their cash. Winchester came in with a syndicate of investors and injected a lot of money into the business. But even with his money, he had trouble acquiring the machinery needed to build the parts for the rifles. That is why the early frames were iron, they were farmed out, perhaps to Colt, because the New Haven factory was not yet capable of making their own frames. Same with levers. There is a reference on that same page about an order of 5000 finger levers being contracted out to the Arcade Malleable Iron Company. Don't forget, production of the Henry was very sporadic up through 1863. It might make sense that if Winchester finally got the equipment he needed in house to make barrels, he might have ceased buying them from England.
P.S. It is really not necessary to whack off the end of a barrel to determine what the metal content is, all that is needed are a few filings. But still, I don't expect anybody to run out and buy an original Henry just so they can make a filings. But I do have references to just that being done with an 1866 Winchester in order to determine the exact metal content of the frame. In fact, I did it myself last year with an Uberti Henry sideplate.