Cotton socks will work as well, but you should make sure that you bring a fresh pair for every day.
The best option for socks is a combination of wool socks and lightweight sock liners made of a material like Capilene. Cotton socks will work as well, but you should make sure that you bring a fresh pair for every day. A good rule of thumb is to bring enough underwear and socks to change them every day even if you wear the same pants the entire trek.