Last year, I did a few hikes in the spring and early summer that included snow travel. This meant that my feet got wet. For those trips, I took two pairs of hiking socks and an extra pair of fleece socks that are significantly bigger than my hiking socks. If both were dry, I wore those socks over my hiking socks. In the morning, I would put on the fleece socks as a way of drying out my shoes. I would basically wear them around camp, thus transferring moisture from my shoes to the fleece socks. When I hiked, I hung up the fleece socks as well as any of the hiking socks that were wet. This worked well.
For whatever reason, I think I ended up using the fleece socks to hike in one day (maybe I only carried one pair of hiking socks on that trip and didn't dry them out) and it worked out fine.