Taanit 13B

אין הבוגרת רשאה לנוול את עצמה בימי אבל אביה. הא נערה ⁠— רשאה.

A grown woman, i.e., a girl over 12½, who is old enough to be married, is not permitted to render herself unattractive during the days of mourning for her father, as this would adversely affect her chances of marriage. The Talmud infers that this halakha applies only to a grown woman, whereas a young woman, a girl between the ages of 12 and 12½, who is not yet old enough to be married, is permitted to render herself unattractive.

מאי לאו ברחיצה, ובמאי? אילימא בחמין, אין הבוגרת רשאה?! והאמר רב חסדא: אבל אסור להושיט אצבעו בחמין! אלא לאו, בצונן. לא, אכיחול ופירכוס.

The Talmud analyzes this halakha: What, is it not referring to the prohibition against bathing? And in what kind of water may a grown woman bathe? If we say that the baraita is referring to hot water, is a grown woman not permitted to render herself unattractive by refraining from washing in hot water? But didn’t Rav Ḥisda say: It is prohibited for a mourner to insert even his finger into hot water for the purpose of washing. Rather, is it not the case that it is permitted for a grown woman to bathe in cold water, from which it may be inferred that it is not permitted for a young woman to bathe even in cold water. The Talmud answers: No, the baraita is not speaking of bathing at all. Rather it is referring to painting the eyes and dyeing [pirkus] one’s hair, which it is permitted for a grown woman to do during mourning.

לימא מסייע ליה, דאמר רבי אבא הכהן משום רבי יוסי הכהן: מעשה ומתו בניו של רבי יוסי בר חנינא, ורחץ בצונן כל שבעה!

The Talmud proposes: Let us say that the aforementioned baraita supports Rava’s ruling. As R' Abba the priest said in the name of R' Yosei the priest: An incident occurred in which the sons of R' Yosei, son of R' Ḥanina, died, and he bathed in cold water all 7 days of mourning. This ruling apparently indicates that a mourner is permitted to bathe in cold water.