Is it obligatory for a woman to cover her head when prostrating outside of the obligatory prayers?

Covering a woman's hair during prayer is obligatory, and the prayer is not valid without it, whether it is an obligatory (fard) or supererogatory (nafil) prayer. This is by agreement among scholars, except that Sheikh al-Islam Ibn Taymiyyah holds that a small amount of hair is excused if it appears, as opposed to a large amount.

As for the prostrations of gratitude (sujud al-shukr) and recitation (sujud al-tilawah), there is a difference of opinion among scholars regarding the conditions of ritual purity (tahara) and covering the 'awrah for them. The safer approach is to observe the conditions of prayer when able. However, others, including Ibn Taymiyyah, are of the view that these are not prayers and therefore do not require the same conditions as prayer.