Double head covering for women?

Question

Is there an inyan for women to have a double covering on their head? (Like men do.)

Answer 1

R. Chaim Berlin has a responsum that addresses this:

Shu"t Nishmat Chaim

Benei Brak 2002 edition — siman 135 part 4

Jerusalem 2008 edition —

ועל דבר כסוי ראש האשה במטפחת אחת אם אין שערה נראין אין בזה שום איסור ועדיף טובא מפיאה נכרית ואין צריך כלל שני כסויין ואם אך אין השער נראה בחוץ די בכסוי אחד אף ברשות הרבים ורשאי גם לקרות ק"ש כנגדה ואין להחמיר עוד בזמן הזה

And with regard to the matter of head-covering for women with [just] one kerchief: if the hair is not visible there is no prohibition whatsoever, and it is better than a wig. And two coverings are entirely unnecessary, and if the hair is not visible outside [of the covering], one covering is sufficient even in the public domain, and it is even permissible to recite Shema in front of her, and one should not be more stringent [than this] nowadays.

Answer 2

The Idea is quoted in this Wiki: http://en.wikipedia.org/wiki/Tzniut#Hair_covering

Hair covering:Three styles of hair covering common among married Orthodox women. From left to right: snood, fall, and hat.Jewish law requires married women to cover their hair;[2][3] According to the Talmud this is a biblical requirement,[4][5] which in this context is called dat Moshe (the law of Moses).[6][7] The most common hair coverings in the Haredi community are the sheitel (wig), the snood, and the mitpachat (Hebrew: scarf) or tichel (Yiddish) ; some Haredi women cover their hair covering *with an additional hat or beret*.