Square_peg has brought up an interesting thing-scrubbing with a brass brush.
It makes quite a bit of sense,and in more way than one:To begin with,brass is softer than steel,which makes it unlikely that it'll score,damage,take away any of the material the axe is made of.
Many axes are covered,partially,with Forge,or Mill-scale,(yet another)form of Ferrous Oxide that is,of course,a by-product of the manufacturing process.
Lets remember now that (most)oxides are Way harder than steel(oxides of different metals are commonly used as abrasive compounds because of that).
Forge scale comes in two general flavors,the loose kind,and the dreadfully STUCK kind,that won't come off for love nor money.....they normally form a patchy kinda pattern over the surface of a forging.
Scrubbing with a steel wire-wheel can actually erode steel from in between the stuck patches of scale,scale being much harder than the wire-wheel,Or the axe itself,so something has to give....And it won't be the super-hard scale!

So,the brass wire is of course much different,way gentler,and won't do that.
But....("Why does there always have to be "but"?"...R.Brautigan,1967)....
Brass is so soft,that some brass(depending on the alloy,all brass is not created equal,of course)will deposit itself on both the steel and the scale(which is also porous,and rough).
If you wire brush long enough,Or,at some moderate heat,pretty soon the entire surface will turn "golden",it'll be coated with brass...
(for a number of years i've forged a carpenter's holdfast with a leaf finial,and many customers requested that the finial be "brassed"...gaudy,but,what the heck

The brass coating will significantly affect corrosion resistance,i think it's (cuprous)oxides spread,protecting the surrounding steel even if the coverage is not 100%...
In the centuries past,many European cultures,notably Germany,had a tradition of "coppering" their tools...Just like that,mechanically,in the Middle Ages,and then later by electro-depositing....You still see a few old "coppered" engraving hammers and measuring instruments....mostly the more costly,precision tools...
Sorry for the rabbit trail....