I have answered a similar question in a different subreddit some time ago. I can't find it though, so let me repaste it from my backup notes:

Most of Europe north of Alps is quite humid, especially in the West due to the influence of Atlantic, so the problem was rather common if not that much of a burden. First and foremost, knights used their armour not that often as one might think. There was little point wearing full suit or even more cumbersome forms type of armour on a daily basis, what limited the possible exposure to the elements. Until late 14th century, armour (or at least the breast- and backplate) were often covered with fabric or leather, first as a structural feature, and later, with the rising popularity of plate armour, as a decoration. This offered at least some protection from the elements.

But even the armour standing in the castle would start to rust, sooner or later. This was mitigated by regular scrubbing of weapons and armour with sawdust and sand. Chain armour was usually put in some container with such materials and moved vigorously to remove rust. Later it could have been inspected and scrubbed by hand if the rust remained somewhere. Then, the armour was usually coated with some substance preventing contact with water vapour, such as oil, varnish or paint. There are some mentions of the high-medieval armours (most likely chain) being cleaned by putting them into sacks and rolled or beaten with thick rods. This is sometimes interpreted as the usage of sacks made sheepskins sewn with the hair inside, so that the kneading of such skin would deposit natural lanolin on the metal object inside. This is possible, as sheepskin was often used as the lining of the well-made scabbards to keep weapons from rusting.

Last but not least, at least some armours were oil-blued, i.e. heated them to about 350 degrees Celsius and doused in oil. This required a decent skill so that the armour would not be heated to critical temperature when it loses its hardness (it is not that easy without thermometers as when the metal starts to glow it is generally too late). Another method was blacking usually conducted by immersing the armour in vinegar so that it rusted slightly, and then boiling metal in water to change the iron (III) oxide into much more stable and less penetrating iron (II,III) oxide. There are also mentions of brushing the hoof of a dead animal over the surface of heated plate armour, but these are unclear and it is not exactly known whether this was actually done and if yes, what was the purpose of this treatment (some suggest it was a form of decoration, others point that this would deposit a layer of keratin that would protect metal from rusting.

It should also be noted that cleaning of the armour was also conducted by specialists, usually local armoursmiths (or, quite possibly, their students and apprentices) as this form of service is often found in ledgers or similar documents. It usually was quite an expensive service, costing a non-negligible fraction of a new set of armour, so we can safely assume that this was an equivalent of a general overhaul, usually involving replacement of damaged or worn metal and leather elements. Of course, it is also possible that such professionals were engaged primarily by urban commoners who were required to possess weapons and armour but generally did not have servants trained in armour maintenance.