I have seen someone put dry socks on and put foot in a plastic bag before stepping into the boot. That might keep your feet dryer a little longer, at least until the sweat builds up.

Never tried it myself though. No snow where I usually hike. And when my feet and boots do get wet, I try to air out and change socks or change into a pair of sandals without socks while the boots dry out. But sandals probably wouldn't work too well in the snow.