Is swimming permitted on 17 Tammuz? Technically speaking says the Debriciner Rov, Rav Moshe Stern in Shu”t Be’er Moshe (3:73) it is permissible. The Shulchan Aruch paskens (550:2) that bathing is permitted on the three Taniyos (Tzom Gedalia, Asara B’Teves, and Shiva Asar B’Tammuz). Although the Acharonim argue on the Michaber and our minhag is to be Machmir, the Pri Megadim says that we are only Machmir for hot water but not cold water.
It can be argued that swimming should be assur because it is Rechitzas Taanug, bathing for pleasure, which the gemara Taanis (13a) seems to assur. However the Debriciner Rov says that Rechitzas Taanug is only assur when the actual bathing is enjoyable, such as in hot water. If the water is cold, yet you manage to find a way to enjoy yourself, that is not called Taanug.
He ends the tshuva by saying that maybe (mourning the destruction of) Hashem’s house merits being extra stringent even when the Halacha does not prohibit it.