Impermissibility of performing ablution while naked

1. Performing wudu is not an excuse that permits one to uncover one's nakedness

The general rule is that it is not permitted to be naked even when alone, except for a reason. The scholars of Sacred Law mention that taking a shower qualifies as a reason, as do other things, such as extreme heat or itchiness. Shaykh Hasan al-Kaf mentions in his book al-Taqrirat al-Sadidah that performing ablution does not qualify as a need, even when this is the sunna ablution before performing the purificatory bath. It would therefore be obligatory to cover one's nakedness when performing ablution.

2. A wudu performed while naked will nevertheless be valid

Although it is necessary to cover one's nakedness during ablution, if one does perform ablution without covering it, one's ablution remains valid and one does not have to make up prayers with such an ablution.

And Allah knows best.

Hamza.