Roll with plastic fenders and mud flaps. If you have to ride in slush, it won't completely cover you or the bike.

I park inside (typically in my classroom, on a cardboard box if its super duper wet. I oil my chain when it starts making noise (usually that gushing noise that happens before a squeak), and grease bearings twice yearly - in Octoberish and Marchish. As for the frame - all of my bikes are steel, and I haven't noticed any appreciable rust on any of my frames due to slush, rain, or salt/grit.