Hi. Thanks for the question. This is a long answer, so I'll put the Tl;Dr at the top: No, it is not true

Great, let's get to it.

1. This claim is rather logically suspect. After all, the prohibition would likely apply to men and women if this were the case, and that doesn't appear to be true.

2. History doesn't back it up. By "recently", I assume you mean within the last few centuries. If this were the case, then we would find few references to this in older texts. However, this does not appear to be the case. The Hadith refer to several instances

Narrated Aisha: The woman is to bring down her covering from over her head and [then place it] upon her face. Bukhari:6:60:282

(The arabic word for covering here is a full body covering)

Muhammad narrated: "And if one of the women of Paradise looked at the earth, she would fill the whole space between them the earth and the heaven with light, and would fill whatever is in between them, with perfume, and the covering of her face is better than the whole world and whatever is in it". Bukhari:8:76:572

The Apostle of Allah used to offer the Fajr prayer and some believing women covered with their covering sheets used to attend the Fajr prayer with him and then they would return to their homes unrecognized. Bukhari:1:8:368

Sunni Islamic law is, by historical circumstance, dominated by four scholars that all also comment on the need for covering. These scholars ( Hanafi, Maliki, Shafi'i and Hanbali) lived between the 8th and 9th centuries, and each of them comments on what is acceptable in terms of covering for women. (By comparison, Muhammad lived in the 600s) [See Hallaq below for more information].

3. Even if these schools of thought require skin covering, this does not mean that Islam requires skin covering. Because of the lack of central religious authority in Islam, anything that is not directly in the Qur'an is up for negotiation. The Qur'an does not say that all women must wear full body coverings. Moreover, there are several Hadith that contradict the ones I cited, and suggest that it is not mandatory and sometimes not even encouraged to wear full body coverings.

Here are some sources which go into more detail. I especially recommend the first, which is highly readable for someone interested in Islam.

Aslan, Reza. No God but God: The Origins, Evolution, and Future of Islam. New York: Random House Trade Paperbacks, 2011. Print.

Goldziher, Ignác, and Bernard Lewis. Introduction to Islamic Theology and Law. Princeton, NJ: Princeton UP, 1981. Print.

Hallaq, Wael B. The Origins and Evolution of Islamic Law. Cambridge, UK: Cambridge UP, 2005. Print.

Korteweg, Anna C., and Jennifer A. Selby. Debating Sharia: Islam, Gender Politics, and Family Law Arbitration. Toronto, Ont.: U of Toronto, 2012. Print.

Zempi, Irene, and Neil Chakraborti. Islamophobia, Victimisation and the Veil. N.p.: n.p., n.d. Print.

Does anyone have any good accounts of the style of dress common amongst pre-islamic Arabs? I know ancient Mesopotamians are depicted as often having uncovered arms and heads with the rest of their body largely covered, but that is the extent of my knowledge.

Additional question: Men wear all white, while women wear all-black (blue in some places, too). Seeing how white is more comfortable in high temperatures, why was white never used for women as well?

Follow up question: Did the religious mandates for woman to cover themselves exist in pre Islamic Arab societies or where they first introduced to the area by Islam?