I'd think the rice would work if you had the saws completely sealed in something that is air-tight(or close to it). If it's just a loose tarp draped over the top, that rice isn't going to work for long with constant, never-ending humidity.
For comparison's sake, I had a cheap BBQ grill that I kept on my deck, always covered in a tarp and it got pretty rusty after 3-4 years. The next one I decided to keep in my shed with my lawnmower and all my yard equipment, in the hopes that would make it last longer. Still covered it in a tarp but it ended up getting rusty in like 4-5 years. So the shed thing did help a *little*, but it was nothing compared to keeping it somewhere that is actually climate controlled like a garage. Our climate here in Missouri is pretty similar to what you were describing, freezing down to 0-ish in the winter, up to 90s and the occasional 100s in the summer with high humidity.
I'm not sure why the lawnmower and lawn equipment don't have issues in the shed, I guess they are built assuming people are going to store them outdoors a lot of the time, whereas something like a table saw or other power tools aren't built with that in mind.