Couple of Lubricants that I have experience of in the wet- Finish line is one of them and the other is Pedro's Syn Lube. Both are a wet oil but can get washed off very easily in Snow. If out for a longer ride- then I take a small bottle with me and re-lube after a while. As to after ride treatment. WD 40 will get rid of the moisture in the chain- but I find it is better to Clean the chain regularly. If you lube the chain and the oil goes Black- then you have a dirty chain. Wash it with a cleaning fluid- I use a chain device and "Muck off"- a general bike cleaner- then I wash off with water and then I use wd40. Leave it for a couple of hours and then lube.. Now if you want an oil that will stay on in Mud and snow- keep looking as I don't think there is one.
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How long was I in the army? Five foot seven.
Spike Milligan