The steel was not dyed or painted, it was "blued" or "blacked". This process is of uncertain origin, but it is very old, as it can be found on Portuguese swords from the XV century, specifically naval swords, and that is important. The bluing technique, which would normally result in a black coating, was produced by heat treating the steel to some 400º C, and then quenching it in very specific oils, which would produce this outer layer of black material, which is ferric oxide. This coating in ferric oxide or other ferric by-products protected the metal from rust and corrosion, hence the importance for naval weaponry. This type of Portuguese swords are called "espadas pretas de bordo" which translates as "black boarding swords". On ships, with all the humidity and salinity, steel or iron would rust very quickly.

The bluing or blacking technique was mastered by some of the greatest armourers of the XVI century, such as the Helmschmid family from Augsburg, or the Negroli family from Milan. The blackening or armor would give the gold ornamentation more prominence, making it contrast more against a dark background than against the silvery ordinary colour present in steel. Sadly, with the passage of time, and with cleaning and restoring, the blackening has faded away and/or been polished away. If you want to know what the armour looked like back in its day, you should check the portraits, and contrast with the current state of those armours.

If you are very interested in this, I mightily recommend you travel to Madrid and visit the Royal Palace, specifically the Royal Armoury, which contains an impressive amount of XVI and XVII century arms and armour some of which still have a darker colour, evidencing that it had been blacked in its day, like this one from 1550 made by Desiderius Helmschmid for Philip II of Spain.