Tools rust in an unheated shed mainly because of condensation, not because the air is generally damp. When the temperature drops overnight, moisture condenses onto cold metal, and a tool sitting at outdoor temperature in a space that warms up during the day collects water on its surface repeatedly. That cycle does the damage.
Which is why insulation helps more than heating
Anything that slows the temperature swing reduces condensation: insulating the shed, keeping tools in a closed cabinet rather than open on a wall, or simply putting them in a drawer with a wooden lining. A sealed cabinet with its own small mass of air changes temperature far more slowly than the room around it.
Keeping tools off outside walls and off concrete floors helps for the same reason, since both stay colder than the air and anything touching them does too.
Dealing with rust you already have
Surface rust, the orange film that wipes to a smear, comes off with fine abrasive and oil. Work along the metal rather than across it and stop when the metal is clean rather than polishing for its own sake. On a plane sole or a saw plate, smoothness matters more than appearance.
Pitting is different: that is rust that has eaten into the metal and left craters. It can be cleaned but not undone, and on a cutting edge or a plane sole it is a real defect. Clean it, oil it, and accept it.
Oil, wax or nothing
A thin film of oil on bare metal is the simplest protection and wants renewing every few months. Paste wax lasts longer, does not attract dust in the same way, and suits tools that are handled, since oil transfers to your hands and then to the work. Either is far better than nothing.
Avoid anything that leaves a thick sticky coat on a tool you use regularly, because you will spend more time cleaning it off than you saved.
Wooden handles and bodies
Wood moves with humidity and metal does not, which is why hammer heads loosen in a dry spell and wooden plane bodies go out of true. Store them away from direct heat, keep the handles lightly oiled with a drying oil rather than a varnish, and re-wedge a loose head rather than relying on soaking it, which is a temporary fix that makes the long-term fit worse.
The habit that matters most
Wipe a tool before putting it away, every time. Fingerprints are slightly acidic and leave visible rust marks within weeks on a polished surface. Thirty seconds at the end of a job is the whole of tool maintenance for most people.