A sock is an item of clothing worn on the feet and often covering the ankle or some part of the calf. Some type of shoe or boot is typically worn over socks. In ancient times, socks were made from leather or matted animal hair.
In the name of Allah
Provided that these socks (1) Won't attract the attention of Non-mahram and (2) Do not qualify as Zinah (adornment), they CAN be considered as proper cover for the feet. Otherwise wearing them is in contrast with the meaning and the purpose of Hijab.
Wudu can not be performed on shoes or socks. Wudu has a compulsory part which is wiping over part the head and on the feet. Feet must be uncovered while wiping on them.
If Wudu was not possible for any valid reason then Tayammum is to be performed in which we put our both hands on the soil or sand or stones etc, then wipe over our forehead from upper part of the forehead down to the end of it, then wipe over the outer part of the right hand then outer part of the left hand.