This would be exceptionally difficult, as oxygen is a basic requirement for steel making as we have ever known it. Steel is made from iron mixed with carbon and then heated to melt. Then oxygen is added which burns the excess carbon into carbon dioxide and reacts with all of the other reactive contaminants and brings them to the surface where they can be cupped off as slag. The melt is poured and cooled and you have steel. Early steel processes used air, blast into the furnace with high powered pumps. Modern steel is made with purified oxygen from cryogenic processes (and there are even designs floating around for steel mills which use the turboexpander from the oxygen processing to help generate electricity to drive the mill).
Without oxygen, you'd have to start with very, very clean iron ore (containing nothing but iron and whatever you wanted to alloy with the final steel), and add exactly the right amount of carbon (which is also exceptionally difficult, since carbon is light and the heat will want to make it sublime anyway). Odds are such a steel would still contain so much impurity as to require a second melt in a vacuum arc furnace, which also would dramatically drive up the cost.
While there might be a future making steel like this in space, I'm not counting it as very likely in the slightest to happen in this century.
It's much easier to use exceptionally clean oxygen - the mill could use an oxygen generation process (like a hydrogen peroxide chemical process plant being added to the mill), or by ultrafiltration of the process oxygen (which seems more realistic all told).
