Where I live we have wet winter months. I don't usually ride while raining, but sometimes it starts to rain while you are out or the road is not dry enough from previous days.
What I do is place on a stand my bike, remove wheels and clean them individually, clean the cog with a hard brush and degreaser, and then with a rag. Then I do the same with the chain, finishing with water and drying it. It's important to clean with a brush the inner part of the chain.
After that, I keep the bike on the stand until next day and apply lube before riding. In my case I have Sram Red (well, now it's a mix of Red, Force, Apex and Rival
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