Is it permissible to wipe over the feet instead of washing them during ablution due to pain and harm resulting from water touching inflamed extremities of the feet?

Ablution (Wudu') must be performed with water if possible. If someone is harmed by cold water, they must heat it. Wiping over the feet during ablution is not sufficient unless one has worn socks after performing a complete ablution, and then wipes over them for a full day. Washing the limbs of ablution once is sufficient, while washing them up to three times is a Sunnah.