Have the wife spend the night in the garage and see how she likes it. Now why would she want your tools to live like that?
I keep my tools in a large tool chest and each drawer has a 1/2lb bag of silica gel to absorb moisture.
You will be fine in the garage. My garage is half shop, unheated no a/c. The wife gets the other half in stormy weather. I put in a paddle fan for when I get sent out to the garage in the summer.
Most tools are in a carry box, or in the toolbox. Always line your toolbox with something. I used rags if nothing else. Keep your tools off the concrete... make a separator with anything but metal or cardboard. I have a big 4x8 bench with a huge storage underneath about 3 inches off the floor.