Full disclosure, I am trained as a historian, but the history of Roman metallurgy is not my specialty. That said, the following Wikipedia articles all seem to have compelling sources about metallurgy, smelting and iron working in the ancient world and the Roman Empire:
en.wikipedia.org
en.wikipedia.org
en.wikipedia.org
en.wikipedia.org
According to the Iron article, Cast iron was first developed in 5th Century BCE China and spread to Europe in the Middle Ages/Medieval Period (around the 15th Century/1400s).
Blast furnaces for being able to refine purer forms of iron have been discovered in Europe dating to roughly 1100 CE, and the slag located in some archaeological sites seems to indicate (not definitive) that earlier forms for "Cold Blasting" of iron existed in the first century BCE (just before 1 CE).
en.wikipedia.org
So, can I definitively say that the Romans melted iron to a full liquid? Well, I suppose not since I was not there. The accumulation of evidence from the brief research I have done seems to indicate it was possible, and likely probable that they could. Why do we not have Roman cast iron? Could be the vagaries of what is preserved, or yes, it could be they never made it.
Having said that, the technology was in place by the middle of the Medieval era (generally held to run c. 450 - 1450), and since our argument is about whether or not D&D as a medieval simulator can allow this. I would say yes.
Now, to go back to the OP question. The boots would not be something I would allow as a DM. As already pointed out, if the party rogue can make them, why has no one else thought of this. Also, why even bother, since you can jump over or move at a slower speed to avoid any issues.
Cheers
Edited due to typos and fat fingers.