Hey, Di
I'm in the same situation since I moved to the California coast (not complaining or anything). Just got my stuff set out and I have covered everything with terry towels, no plastic. I have coated all my metal tools with light oil and have put them in covered boxes. My studio is also really no more than a garden shed…or since I don't have a garden, just rocks and a covered sheltered area outside.
It's only been a few days since I set up but I do worry about my kiln also. Today I removed it from the plastic I brought it down in and covered it with a towel because I'm not using it right away. I have an electronic controller. Since it's a Jen-Ken I assume it can withstand some humidity as it was built in Florida and it's way more humid there than here. I'm keeping an eye on things for sure!
My oxycon, also covered completely with a large terry towel.
Crossing fingers.