|Observing the closing havdalah ritual in 14th-century Spain.|
That's a big candle!
This article by Ari Z. Zivotofsky (quite a name) entitled "Wine from Havdalah, Women and Beards" examines the issue in some depth. I recommend you read the entire article, though below I've collected some of the more interesting tidbits from the article:
The origin of women not drinking Havdalah wine (among other halachic reasons he explores):
...The reason originally mentioned by the Shla6 is that because theEitz Hada’at, the tree of knowledge, was a grape vine7 from whichChava squeezed wine in order to separate from man, a wish she wasgranted via dam niddah, menstrual blood, she does not partake ofthe havdalah (separation) wine.
Despite the widespread mention in later sources attesting to thiscustom, it appears to be a custom of relatively recent vintage [Nice Pun!], withthe first written source being the early 17th century. The lack of awritten source does not preclude the possibility that a custom existedbut is simply not attested to in writing.
On the origin of the hair myth:
The closest written source I have found is a cryptic remark in
the “hashmatot section” of Sefer Matamim (Rav Yitzchak Lipiyatz,
p. 242 in 5753 reprint, p. 144 in 1891 edition) where he explains
that it is because women do not have beards that they are prohibited
(!) from drinking the havdalah wine. He offers no explanation
for this seemingly bizarre connection. But one could imagine that
such a statement could easily lead others to conclude that if she did
drink it, she would grow a beard. However, despite the inclusion of
this statement in Sefer Matamim (originally published in 1891), it
does not seem to have been a widespread idea, and I have been unable
to find it recorded elsewhere.
A possible theory:
the Gemara asserts that drinking beer causes unwanted hair on females, and it was
girls who drank beer who required the use of the described methods
to remove the unwanted hair.
In Eastern Europe wine was a rarity. The Aruch HaShulchan
(OC 182:1) explains that despite the halachik obligation, they did
not bentch over wine simply because it was very expensive.21 According
to all opinions chamar medina may be used for havdalah
(MB 271:56). Because of the difficulty in obtaining wine, it is possible
that in Eastern Europe beer was the beverage commonly used.
for havdalah and hence women were advised not to drink it because
beer, not the havdalah beverage, causes unwanted hair. This bubba
meise that was originally based on the specific beverage22 was eventually
ascribed to the ceremony, and the legend evolved that women
drinking the havdalah wine grow unwanted hair