Yes obviously. Indra is stating the rules of women which EVERY SINGLE WOMAN MUST OBEY, including in this part of Rig Veda where even a woman form which has emerged due to a curse definitely HAS TO FOLLOW THESE RULES. I am giving old translations from previous centuries or from village areas several years ago:
तू सदा नीचे देखा कर, ऊपर मत देख, पैरोंको पास रखते हुए चल, तेरे शरीर के दोनों भाग मुख और पिढलियाँ न दिखाई दें, क्यों कि तू ब्रह्मा कि स्त्री थी।। (Translation from -- Govind Bhavan Karyalaya, Gita Press, Gorakhpur)
It means you will ALWAYS LOOK DOWN, keep your feat together & walk, BODY & FACE WILL BE BOTH HIDDEN, because you were Brahma's woman/female.
(इन्द्र ने कहा) प्रयोगि, तुम नीचे देखा करो, ऊपर नहीं। (स्त्रियों का यही धर्म है।) पैरों को संकुचित रखो (मिलाये रखो) । (इस प्रकार कपड़ा पहनो कि) तुम्हारे केश (ओष्ठ-प्रान्त) और प्लक (नारी - कटि का निम्न भाग) को कोई देखने नहीं पावे । यह सब इसलिए फरो कि तुम स्तोता होके भी स्त्री हुए हो (Translation by Pandir Ramgovind Trivedi, Vedantshastri, Varanasi)
It means that it is a WOMAN'S DHARMA to look down instead of up... keep their feet together, cover their bodies etc. Here is another desi translation by Arya Samaj from 19th century:
Again it says WOMEN SHOULD COVER THEMSELVES. Now here is an old English translation from 19th century:
Cast down thine eyes and look not up. More closely set thy feet. Let none see what thy garment veils, for thou, a Brahman, hast become a dame [woman] (Translation by Ralph T Griffith)
Here is Sayana's medieval commentary in Sanskrit -
He also says THIS IS WOMENS DHARMA. So every single woman must be covered except in rare circumstances. Here is a medieval Indian painting:
Here is ancient folk representation of Bengal and other part:
Valmiki Ramayana is dated to at least 4th century BCE it also has mention of headcovering in Yuddha Khanda 6, Sarga 111, verses 63-64. And this part is found in 6TH CENTURY COPY (oldest) of the Ramayana:
“O Lord! Are you not indeed enraged, in seeing me on foot in this way out through the city-gate, unveiled and come on foot in the way? O lover of your consorts! Look at all your spouses, who came out, with their veils dropped off. Why are you not getting enraged in seeing this?” Tr. K.M.K. Murthy
And Hindu marriage also has Ghoonghat as compulsory for women. So anyone saying that headcovering is not in Vedas or Indian culture is wrong.