Is wiping over the leather socks without the ablution being invalidated considered a wipe that does not count towards the wiping period, for those who hold that the wiping period begins after the first wipe following the occurrence of ritual impurity?

The scholars who favored the view that the calculation of the duration for wiping over the khuffs begins from the time of wiping, hold that the period is calculated from the first time one wipes after an impurity (hadath (definition)). So, if one wipes during a supererogatory ablution (wudu mustahabb) not due to an impurity, the calculation does not begin then. Rather, it begins from the first time one wipes after an impurity. This opinion was chosen by Al-Nawawi and Ibn Al-Mundhir, and a similar view was narrated from Umar ibn Al-Khattab, may Allah be pleased with him.