Thanks for the replies.
I already have fenders, but the slush still got everywhere. In fact, it got caked between the fender and the tire, too.
I don't like to lube my chain wi/o a thorough cleaning first -- I've heard that lubing a dirty chain just drive the dirt deep inside it and causes your chain to wear more quickly. I don't have the time or energy to do this after every wet/snowy ride.

I will look into a heavier or wax-based lube. When my current chain wears out (which will be soon, I think), I may try to get a pair of SRAM chains so I can easily rotate them.