I did a MTB race the day after weather like that. It was supposed to rain all night, and it did. I knew the trail well and I new that as it warmed up that mud was going to get all sticky and gooey. I switched out my clipless for rat traps - this was pre-eggbeaters and the spds used to get gummed up pretty easily. I also rode a rigid frame. I actually did well. Not because I'm fast but because I had fewer mechanical issues than most.

All of us threw our bikes in the river at the end. They were trashed. It took me at least 3 hours of cleaning etc, to get my bike back to a point where I thought it was rideable.