Does your garage have any form of damp proofing? If it doesn't have a damp proof membrane under the floor or there's no damp course, or if the walls are porous, then it could get very moist inside. I fixed a similar problem in a garden shed by liberal application of Thompson's Sealant – floor and walls with special attention to where the wall meets the floor.
I don't have a rust problem in my garage which is part of the house and double-skinned, What helps me here is good ventilation and avoiding quick heat-cool cycles.
If you come into a damp cold workshop and put a heater on, water will be forced out of the air and condense on the nearest cold surface – like your tools. Then, as the heater warms the wet tools up, the combination of warmth and oxygen rich damp accelerates rusting.
My garage door leaks air like a sieve and – apart from lighting – I don't heat the workshop. When I start work the damp air warms up slowly and has plenty of time to escape, condensation is reduced, and a cold workshop slows down rusting.
It works for me because I live in the mild South West and dress like Nanook of the North during winter. Doing the same is a single skinned detached garage in the North might be too uncomfortable.
I developed a condensation problem in the sticky-out hall of my house after fitting double glazed windows and front door. It created an unventilated cold spot in the house where centrally heated warm air dumps moisture. There was no problem when the hall was draughty. A dehumidifier helped.
Dave