The custom of the Ashkenazim is to refrain from bathing throughout the Nine Days, from Rosh Hodesh Ab through Tisha B’Ab. Sepharadim, however, follow the practice of allowing bathing until the week of Tisha B’Ab. According to Sephardic custom, one may bathe as usual until the Shabbat immediately preceding Tisha B’Ab. Therefore, this year (5770/2010), bathing is forbidden for Sepharadim only after Shabbat, on Sunday and on Monday, besides, of course, on the day of Tisha B’Ab (Tuesday), on which it is anyway forbidden to wash oneself.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) ruled that bathing during the week of Tisha B’Ab is forbidden even if one uses cold water. However, Hacham Ovadia Yosef and many other authorities disagree with this position, and rule, based upon the rulings of the Rambam, the Ramban, Rabbi Kalonimus’ Sefer Ha’roke’ah and other authorities, that the prohibition applies only to hot water. According to this view, bathing with cold water is permissible during the week of Tisha B’Ab. This is, indeed, the commonly accepted practice. Furthermore, Hacham Ben Sion Abba Shaul (Israel, 1923-1998) ruled that one may add some hot water to the cold water in order to remove the chill and make the water tolerable.
Accordingly, it would be permissible, strictly speaking, to swim in the ocean or in a cold pool during the week of Tisha B’Ab, since the water is not hot. According to Ashkenazic custom, however, this would be forbidden.
Summary: Whereas Ashkenazim refrain from bathing throughout the Nine Days, the custom of the Sepharadim is to forbid bathing in hot water only during the week of Tisha B’Ab. It is permissible to bathe in cold water during the week of Tisha B’Ab, and one may even add some hot water to make the water tolerable.