How to clean a bike after muddy/sandy cyclocross race (or mountain bike ride)

You should definitely be careful with it, but at many races we employ the use of a pressure washer to do broad stroke cleaning like getting mud, grass, etc off the bike and tires. You need to be careful and use it from a little distance and obviously not get up close on the BB, hubs, etc. but it does a good job of initially cleaning or cleaning between races.

After the race you should do more appropriate maintenance on the bike with degreaser and proper lubes.

You should probably start with a bike wash and then regarding the drive train, I would pour warm to hot water on it to loosing any mud and dirt. I would then use a chain brush to loosen any mud or sand and follow it with another hot water wash again just pouring the water onto the cogs and drive train.

Then I would do a normal chain services as outlined below to remove the chain grease and finer dirt.

The steps I use when cleaning components are summarized as:

1. Shift Into the Big Chain Ring and Small Gear in the back
2. Degrease - Chain clean tools made by Park or Finish Line make things easier here.
3. Water Rinse Chain - Chain clean tools made by Park or Finish Line make things easier here.
4. Wipe Chain With Rag
5. Clean Drive Components (i.e. Cassette, Chain Ring, and Derailleur)
6. Clean Cassette (See Above) - Something like a rag wrapped around something thin and solid like a CD works well for me and is inexpensive. A example is shown here in this clip:
7. Wipe Chain With Rag
8. Lube Chain - Only 1 small drop of lube per link. Find the masterlink/quicklink on the chain and use that as a reference to make sure you only lube a link 1 time. Less is more here as unnecessary lube just flings off the chain onto your wheel or braking surfaces and attracts more dust. Some people like to wipe their chain after lubing it, but I have had good luck just sparingly applying the lube to begin with so that after the next step there is not much need to wipe any excess. However, again each person may have their own opinion or preference on the matter. I have had good experience with WD40 Wet Lube (Not regular WD40) and Finish Line Ceramic Wet Lube. I am sure each person will have their own preferences like people do when it comes to motor oil.
9. Shift through all gears and chainrings to spread the lube around.

Just to emphasize a couple minor points:

1. Given that the question specifies rim brakes, I would put a bit of effort into cleaning off the rims and brake pads. Grit will wear your rims down.
2. Again, concerning the rim brakes, there is no way to really clean out the cable housing once dirt has intruded. The only thing I could think of would be to consider cable sets that have some protection against dirt intrusion. For example, Jagwire, an aftermarket cable manufacturer, lists some end caps here that have seals to reduce contamination. I don’t believe these features come stock on Shimano or Campagnolo cables. I've used both. Neither company ever really concentrated on the specific needs of the cyclocross market. Also, rim brakes are dying out in that application anyway, and it is a niche discipline to begin with.
3. Clean chains last longer. Ideally, I would bring an on-bike chain cleaner and some degreaser. Several changes of the degreaser might be needed. The point is to try to get dirt out of the inside of the chain, where it really matters. If willing to remove the chain, keeping in mind that master links can in fact be reused multiple times, you could substitute Gatorade or other drink bottles.

At the one cyclo-cross race I've seen myself and those I saw on the telly bikes were cleaned with pressure washers.

At the Munich race I've seen Pro and amateur's mechanics used the pressure washer station. They used also a rag or towel to flog the bike dry. Canyon works mechanics unshipped the chain right at the pressure washer. (Some spectator picked master links between the wooden planks after the race.)

A pressure washer might be the only way fast enough to get a bike ready before the rider may want to swap bikes again after just one round.*

If a bike's bearings are so badly sealed they deteriorate because of some overspray they might not be quite up to the challenges of off-road riding. What is more, at pro and elite levels riders tend to have thorough maintenance every few races. Sometimes bikes are completely disassembled after every race event.

*The team on Canyon did that for their lead rider. I suppose the sponsor wanted him to compete on his shiny golden Inflite rather than on one with dull team colours.