Thanks for the suggestions. Here's my comments on some of the solutions:

Power Washer - I've done this before, but it really does more harm then good. If you use a car wash powerwasher, use one that has a mist setting.

WD-40 - This isn't a lubricant. You really shouldn't use it on your chain. Lots of people do, I know, and if you think it works, go for it.

My plan is to hit up Home Depot for some Simple Green and a large tub. I'll do a quick once-over outside, trying to get the majority of the caked on mud off outside. Then I'll give it a quick drydown and bring it inside. I'll use the basement if it isn't too cold down there. I'm going to set the stand up on a bunch of newspaper and go to town with a spray bottle of simplegreen. I'll have the chain off for this and will remove anything else I think i can easily enough put back on. When I re-assemble the bike, I'll put fenders on it to keep it from getting this dirty again.