Clay is a pain when it dries. But once it does, you can knock the majority off with the back end of a big screw driver. and for the car, you can chisle it away with a screw driver and hammer or other tool.
Carefull about doing it in the sink. I have a basement sink that is meant for heavy cleaning, but it has 4 Inches of mud in the bottom of it and I've had to use draino too many times when it gets backed up. All from one muddy run.
I just DON"T run in the mud anymore. If its sopping wet, I don't run! Thats the best way. Its just not worth it.
Water will ruin standard foams quickly! Molded foams are too heavy so I don't run them PERIOD. So, I use a bucket of water and Simple green. I spin the tires with the tread only, hitting the water. So no water gets inside the tires through the rim holes. And clean them with a brush while rotating them through the top of the water to rinse. You just have to take your time and be carefull not to submerge the rim under water. Even the bead will alow water in so you must be carefull.
We grass works very good BTW
