I apologize for the brevity, but I really don't know how to write anything longer on this topic. Rust is an issue for anyone who works with metal. Armor and weapons are certainly prone to corroding. Advanced treatments like bluing parkerizing and stainless steel didn't exist. We do have some evidence that armor was sometimes painted, possibly to prevent corrosion, but mainly for looks. Luckily, as a member of the lower nobility, you almost certainly have a dogsbody with you to see to your kit. Grease could be used to protect metal, and sand and vinegar were used to remove rust.

The other responses here are great. One thing I might add is that much medieval iron had a very high phosphorus content. Phosphorus does a few things to iron. It makes iron more brittle in colder temperatures ("cold short"), so we generally try to remove phosphorus from modern alloys. It also, however, makes iron much harder -- up to three times as hard as plain / pure iron, as hard as inexpertly worked carbon steel, and about half as hard as an expertly hardened and tempered steel. Because much early medieval steel was inexpertly worked, phosphoric iron was a smart choice for blade edges.

Phosphoric iron's other property is rust resistance. This probably meant that many early medieval blades and armors didn't rust as quickly as modern carbon (non-stainless) steels.

It was a problem for anyone who kept weapons or armor, and a significant contribution to the labor necessary to keep the equipment of a soldier or a knight ready for battle. Stainless steels are a relatively recent invention, and not entirely 100% proof against rust even so. A lot of equipment used by a knight or soldier would have been made of iron or steel, plate and chain mail (as well as other varieties of mail), swords, knives, axes, hammers, spears, arrowheads, and so forth.

Typically there were various different methods for removing rust from pieces and then protecting the metal from rust with an application of some protectant, typically just oil. For example, caring for a sword might involve regularly sharpening it, wiping it down with oil, and returning it to a scabbard. Even just regular handling, let alone training, would wear off the oil residue and contaminate the sword surface with potentially water, dirt, or skin oils (which are slightly corrosive to metals) so regular maintenance is also a must. Similar work would be done to maintain full plate armor whereas stuff like chain mail might be tossed into a barrel along with some sand and tumbled until the rust had been removed.

There's more info from a post by u/Taliesintroll nearly a year ago here: https://www.reddit.com/r/AskHistorians/comments/44fqpe/how_did_roman_and_medieval_armies_manage_rust_in/