I was at a carnival, and they added those little chips of wood all over the place because of rain. Can you sweep puddles on grass? I don't know. I never tried it. Pinetar has a point though. If you just stand by, and do nothing you have the mindset, just forget it. Even though the solution might be impractical, you are least trying. I have a vacuum that takes in water, and than you can dump it elsewhere. It might sound stupid, but it could have got rid of your puddles. It's at least trying.
To me, I kind of think you have a reason to close up shop though, but there was a carnival around Chicago who after one day of rain, said we are not opening at night even though the fields weren't wet, and there was no mud either. That's ridiculous in my opinion, and they are gone because of that.