I tried to avoid submerging my feet in the slush to such a depth that the cloth part of my shoe (which starts above the bottom rubber part) got wet. Still, even walking part of the way to school with the guy adds up to around half a mile, so I did end up with wet socks.
Then, I pulled this power move: I took my post-workout change of socks out of my backpack and changed into them right there on the platform at Porter. I got changed by the time the train arrived, and my feet feel dry and toasty as I stand here on this train right now.