As you can see, frequent re-lubrication of the chain is pretty important.
I live in Portland, Oregon. Lots of rain. Not quite as much as Seattle is famed for, but almost!
After riding in the rain, I plug in my air-compressor. While it's running, I quickly run low-pressure water over my bike, from top to bottom and try to stay away from the seat-post collar and headset. I have a set of Park Tool cleaning brushes. I may use one of these to dislodge heavy road-grime from the bottom bracket or down-tube. I don't bother with soap-- next ride will likely be just as wet and messy. Even when mud is involved, soap is a waste. The bike will get dirty in another couple of days.
Once I'm finished rinsing the majority of the dirt off the bike, i bring the air-compressor over and blow-dry the chain. I direct the air from the cog-side of the chain to blow contaminants OUT of the chain.
The rest of the bike gets a quick wipe down with a shop towel.
I apply ProLink Gold lube to the chain. It hold up really well in all kinds of weather and beats the tar out of anything else I've used (Pedro's SynLube, White Lightening wax-based stuff, Finish Line, A.T.B.). It is a liquid that penetrates the link and rollers quickly.
This whole procedure takes maybe 10 minutes. Considering that this gets done after every ride during the winter months I don't want to spend a disporportionate amount of time cleaning every little nook and cranny and getting the bike sparkly clean.
Important point: A little bit of clean done regularly goes a long way. Focus on the drive components-- cassette, chain, cranks, derailleurs.
Once spring is firmly in place and it's not raining constantly, THEN the bikes all come out for a soapy spring cleaning complete with silicone polish (Pedro's Bike Lust spray). I use plain liquid dishwashing soap (a generic equivalent of Dawn) to clean the bike. Cuts grease and oil, non-toxic, and leaves my hands oh-so-soft. Plus makes everything smell apple-y or lemon-y, depending on the soap i use.