In this answer it is mentioned that head covering allowed only certain instances but not during worship.
But we do see priests wearing turban when carrying utsava murthy for proceedings, like in the attached image from Sringeri mutt.
In what situations one must wear head scarf or turban?
I know it’s late but at least it’s better to have a answer then never
I did some research on Wisdom Library and I found out this:
This is first from 2.1 of Cosmetics, Costumes and Ornaments in Ancient India:
The term Uṣṇīṣa is defined thus–
[...],[2]
Meaning that which keeps away heat. It is a turban made of a lengthy cloth and was worn in different modes. Uṣṇīṣa was prevalent since Vedic times. The earliest reference to it is found in Ṛgveda[3]. Both men and women wore Uṣṇīṣa. On the basis of their status, people wore different types of Uṣṇīṣa. It was of different colours. During religious ceremonies wearing Uṣṇīṣa was compulsory. From Kātyāyana-śrautasūtra[4] we learn that Uṣṇīṣa was worn in such a way that lots of cross windings were produced in it. For the sacrificial ceremonies, it was worn in a different method.
In Atharvaveda[5], Yajurveda[6] and in Brāhmaṇas[7], we have reference to Uṣṇīṣa worn by Vrātyas and kings. Vrātyas wore white turban. Kings wore Uṣṇīṣa on the occasion of Vājapeya and Rājasūya. But we get no evidence to women wearing Uṣṇīṣa, except Indrāṇī mentioned in Ṛgveda[8] and in Śatapatha-brāhmaṇa[9]. On this basis Dr. Altekar has concluded that Uṣṇīṣa was worn by women of high social status in that period. From Baudhāyana-dharmasūtra[10] we learn that Uṣṇīṣa is a must for a Snātaka. Āpastamba-śrautasūtra[11] recommends a white turban for a king who performs Rājasūya. In Purāṇas[12] Śiva is described in several places with Uṣṇīṣa having colours white, yellow and black. Similarly, Brahma is depicted as wearing a white one. From Mahābhāṣya[13] we learn that priests wore Uṣṇīṣa of red colour. We have reference to Uṣṇīṣa in the epics and in the works of Bhāsa[14], Śūdraka[15] and Daṇḍi[16].
Reference to Uṣṇīṣa often occurs in Purāṇas in the descriptions of gods as well as Rākṣasas. In Matsyapurāṇa[17], white clouds are compared to the Uṣṇīṣa of Himālaya. Unlike Vedas, there are rare mentions of Uṣṇīṣa worn by women in the epics. But they are often described as covering their hair either with a separate cloth or with the end of their lower garments.
Bṛhatsaṃhitā[18] attests the use of Uṣṇīṣa by a priest performing Homa. It is stated in the text that seeing Uṣṇīṣa on morning or at the commencement of a journey is considered auspicious.
This is from 2.24:
As in Brahmaṇas, we have reference to grass garment in Kātyāyana-śrautasūtra[10] also. There during the performance of a Vājapeya, the sacrificer’s wife is suggested to wear an underskirt namely Caṇḍātaka. It should be made of Kuśa grass. Similarly a king who performs Rājasūya is recommended to wear a Tārpya, Adhivāsas, Pāṇḍva and Uṣṇīṣa.
This another quote from 2.2 of another Book called Atithi or Guest Reception (study):
Ceremonious purchase of Soma in Somayāga is known as Somakrayaṇa. Somakrayaṇa is performed in Uparavadeśa.[5] In this ritual, Soma stalks are placed on a bullock skin and guarded by a helper. Adhvaryu stands to the west of the Soma bundle and Kautsa[6] to its east, facing each other. The Adhvaryu asks Kautsa
whether his Soma is pure,[7] Kautsa replies that it is. The Adhvaryu measures it, with different fingers, with and without mantras.[8] The Soma is then folded in a cloth and the Kautsa places it on his head. Then Adhvaryu bargains with Kautsa for the Soma.[9] Finally Adhvaryu takes Soma from Kautsa and places it on the right thigh of the Yajamāna. At that time Yajamāna, bestows his headware (uṣṇīṣa) to the Soma. This is to show Yajamānā’s respect to Soma as here Soma is treated as a King. King always deserves respect.
हर हर महादेव जी ਹਰ ਹਰ ਮਹਾਦੇਵ ਜੀ जय जय सनातन धर्म ਜਯ ਜਯ ਸਨਾਤਨ ਧਰ੍ਰਮ
