One of the things my son hated for the longest time was socks and shoes. I couldn't keep them on his feet and it was a constant battle to get him ready to go anywhere. There were times that I simply had to take him shoeless and sockless with me because there was no way I was going to buy seamless socks when we already had some.
Some of the solutions that we tried that worked was turning his socks inside out so he didn't have the fuzzies on the inside. We got some socks with different textures such as dress socks and tube socks rather than they typical sport socks. Turning them inside out helped him for a while if he HAD to wear something on his feet. I hated him being in shoes without socks because he would ruin them.
The only other alternative that worked was getting shoes he could wear without socks. Crocs worked the best for us although I bought the cheap brand. He could wear them without having socks on and they were easy to put on. If your child doesn't like crocs then you might try sandels or aquasox which the tightness can be adjusted on sandels and aquasox are tight anyway. Crocs, sandels and aquasox were meant to be worn without socks so it works perfect if you don't want ruined shoes by little bear feet.