They can if they'd like to, but they're unable. The kind of mud they're dealing with is very slippery, so, unless you bring a vehicle specifically designed for it, you're not going to be able to drive on it without being sunk up to your axles.
"Please do NOT drive at this time. Road conditions differ based on the neighborhood. We will update you on the driving ban after this weather front has left the area.
It will hamper Exodus if we have cars stuck on roads in our camping areas, or on the Gate Road out of the city. PLEASE don’t be that person. The roads will dry. The issue is NO LONGER ruining the roads (that is the concern before we start the event), but once we are in Exodus we need the roads to be clear, and not to have vehicles blocking traffic flow."
(If you brought them along on a spare set of rims and swapped them when it became clear what weather was coming)
Usually paddle tires (the ones with scoops) are used in sand, not mud.