Generally they do very well. A funny thing is that I've run into the death-mud in cottonwood as well, so it's not just here. Anyways, do not ride 347, or if you do, do not ride it past the intersection of 348. I realize that a lot of people like this mild downhill and mild "jumps", but it's not going to be worth it when you run into the death mud.
On the other hand, 351, 352, 345, 349, 350, 40, and I think 332 (it's fairly new and I'm trying to remember if I've ran into it there, it might be possible near the gate from 346) are allways clear and good to go in my experience. No issues.
Watch out for 347 at both extreme ends, the top of 346, 308 and DO NOT EVER start in Williamson Valley when it's rained recently. Those are the death-mud trails, but there's plenty to ride in Granite Basin when it's wet.
Picture of death mud in cottonwood
Picture of death mud in granite basin (bonus points for finding the wheel in the picture)