Pretty simple solution, bring it back inside when you're done using it for the night and don't expose it to rain. If you want to leave it out set it on a stepping stone block and flip a black tote over on top of it.
We use a water proof tarp which is painted like a rock on one side- that goes over one fogger and chiller. The other fogger sits under a milk crate, which in turn sits inside a plastic bag. The bag keeps the water off the fogger, and the milk crate allows ample airflow so the plastic doesn't melt. The nozzle for the fog comes out where one of the handles used to be.
There are quite a few ways to protect it from the elements, and you've been given the basics of "don't leave it outside when you're not using it" and "stash it under a tote bin."
However, if you want to get fancy, I've seen folks build fake boulders, coffins, and tombstones to act as weather resistant covers for their fog machines. In fact there are plans kicking around online on how to build a fog machine toe pincher coffin with built in fog chiller.