Honestly, it depends upon the Muslim you talk to.
I have met some that say it is a requirement and other that say it is totally voluntary.
And say to the believing women that they cast down their looks and guard their private parts and do not display their ornaments except what appears thereof, and let them wear their head-coverings over their bosoms, and not display their ornaments except to their husbands or their fathers, or the fathers of their husbands, or their sons, or the sons of their husbands, or their brothers, or their brothers' sons, or their sisters' sons, or their women, or those whom their right hands possess, or the male servants not having need (of women), or the children who have not attained knowledge of what is hidden of women; and let them not strike their feet so that what they hide of their ornaments may be known; and turn to Allah all of you, O believers! so that you may be successful. . (Qur'an 24:31)
Those who harass believing men and believing women undeservedly, bear (on themselves) a calumny and a grievous sin. O Prophet! Enjoin your wives, your daughters, and the wives of true believers that they should cast their outer garments over their persons (when abroad) That is most convenient, that they may be distinguished and not be harassed.
And Allah is Oft-Forgiving, Most Merciful. (Qur'an 33:5859)
O Wives of the Prophet, ye are not like any of the (other) women. If ye do fear (Allah), be not too complaisant of speech, lest one in whose heart is a disease should be moved with desire: but speak ye a speak that is just. Abide still in your homes and make not a dazzling display like that of the former times of ignorance: and establish regular prayer, and give regular charity; and obey Allah and His Messenger. And Allah only wishes to remove all abomination from you, ye Members of the Family, and to make you pure and spotless.
Communicate what is taught to you of the verses of God and the wisdom revealed by Him [to your visitors]. The Almighty is very discerning and all-knowing. (Qur'an 33:3233)
O Ye who believe! Enter not the dwellings of the Prophet for a meal without waiting for the proper time, unless permission be granted you. But if ye are invited, enter, and, when your meal is ended, then disperse. Linger not for conversation. Lo! That would cause annoyance to the Prophet, and he would be shy of (asking) you (to go); but Allah is not shy of the truth. And when ye ask of them (the wives of the Prophet) anything, ask it of them from behind a curtain. That is purer for your hearts and for their hearts. And it is not for you to cause annoyance to the messenger of Allah, nor that ye should ever marry his wives after him. Lo! That in Allah's sight would be an enormity. (Qur'an 33:53)