Socks serve two purposes: to wick sweat away from skin and to provide cushioning. Because of this, cotton socks aren’t very good for hiking, except in extremely dry environments, as they trap moisture that can lead to blisters.
Wool socks or liner socks work best, so you’ll want to look for three-season socks, also known as trekking socks. While a little thicker than summer socks, their extra cushioning generally prevents blisters.
Also, make sure kids don’t put on holey socks; that’s just inviting blisters.
Read more about day hiking with children in my guidebook Hikes with Tykes.