You can prevent or at least greatly reduce this by wiping the chain dry at the end of the day. Even better -spray some WD40 on the rag first. Spray a bit on the cassette too. The topic of chain lube is inexhaustible, so I will just offer 2 thoughts.

- Some of the 'wet' lubes recommended for winter use are extreeeeemly messy. I used Finish Line Green for a while and it is indeed tenacious and protects the chain well; but it becomes a black crawling horror that spreads around the bike and is difficult to remove.

- This year I'm trying Boeshield T9 and so far it seems like a good compromise; it lasts reasonably long in wet conditions, protects the chain reasonable well and isn't hard to clean up.