When the whole bike is muddy -- like right now, after some recent rains and riding on muddy gravel -- I use hot water and Dawn on the whole bike, including the drive train.

Squirt WD-40 onto the chain to displace water. It works just as described, never had any problem with residual water causing rust.

Finish up with whatever chain lube I have available -- Park CL-1 at the moment. Might try Chain-L later.

I'm about to try either a Nashbar chain cleaner or the White Lightning chain cleaner doodad for more routine quick cleaning. I tend to put off chain cleaning until it's really grungy. Bad habit.

I probably oughta use a quick link too. Easier to clean both the chain and front and rear sprockets with the chain off the bike. I did that years ago with my road bike, never had any problems. I should do it with my hybrid as well since I'm riding gravel more often now.