Bathing/Showering in cold water:
The Sages did not decree against bathing in cold water on Shabbos and it is thus permitted to do so from the letter of the law. Nevertheless, the custom in the Ashkenazi provinces is to avoid doing so being that there are many bathing restriction involved which people are not aware of. [This custom has been around for many generations dating back hundreds of years, and one who comes to break the decree of the Rishonim on him it says “Yashchenu Nachash”, as we have accepted this custom as a complete prohibition not to bathe in rivers, lakes and ponds at all on Shabbos. This prohibition applies even against bathing in an enclosed area, such as inside a house and the like, and is not limited only to a river. This applies even against showering, although in a time of need one may be lenient to shower as explained in the Q&A below.]
The bathing restrictions:
- To dry oneself so no water is carried outside [in a place without an Eiruv].
- Not to swim in the water.
- Not to splash away debris.
- Not to squeeze ones hair. Regarding details of this restriction-See Halacha 5 Q&A there!
May one take a cold shower on a very hot day?
Although in general it is forbidden to shower on Shabbos even in cold water, nevertheless if one is bothered by the heat or the perspiration then he is allowed to shower in cold water [or warm water that was heated before Shabbos].
Hot water: To shower in hot water heated from before Shabbos is only allowed if one is in pain, as will be explained in Halacha 3 Q&A there. As well as one must take care not to transgress the cooking prohibition through turning on the hot water tab, as explained in “The Laws of Cooking” Halacha 9 Q&A there.
 326/1 and 6; Michaber 326/1; Shabbos 40a
Water in a vessel: It is permitted to do so even if the cold water is within a vessel. [Setimas Haposkim that only prohibit the hot springs that are within a vessel and not cold water; Implication of M”A 326/8]
Other opinion: Some Poskim rule it is forbidden to bathe in cold water that is in a vessel. [Mordechai, brought in M”A ibid]
 326/6; M”A 326/8; Bach; Maharil 139; Terumos Hadeshen 255; Beis Yosef Y.D. 199; M”B 326/21
Other opinions and Sefaradic custom: Some Poskim rule that today the custom has spread to allow bathing in cold water. [Olas Shabbos 326/16] Accordingly, some Sefaradi Poskim rule it is permitted to bathe in cold water. [Or Letziyon 2/35-2; Implication of Rav Poalim 4/12 and Y.D. 15 regarding a shower, however see Yaskil Avdi 6/1 who is stringent] Practically, each community is to follow his custom. [Kaf Hachaim 326/25 and 31] This custom is omitted by the Michaber and Rama, although is mentioned by the Beis Yosef ibid
When does the custom apply? Admur ibid writes “Due to that not everyone knows to beware in all the below mentioned matters, therefore the custom spread in these provinces to not bathe at all on Shabbos.” From this wording it is implied that only when all these suspicions are applicable are we accustomed to avoid bathing, however from the concluding wording of Admur “therefore the custom spread in these provinces to not bathe at all on Shabbos, not even with cold water” it is implied that the custom spread to all items. Perhaps this is because the main worry which brought about this custom is that one may come to squeeze the hair, and so writes Beis Yosef and M”B ibid; However see Ketzos Hashulchan 133 footnote 8 that the decree only applies when all the suspicions are applicable.
 Aruch Hashulchan 326/9
 Implication of Admur ibid “therefore the custom spread in these provinces to not bathe at all on Shabbos, not even with cold water”; M”A ibid in name of Maharil, Mordechai and Beis Yosef which states that even a Mikveh is not used for this reason, and a Mikveh is usually in an enclosed area; M”B 326/7 “In a river or Mikveh due to squeezing of hair”; Minchas Yitzchak 6/32; See Shabbos Kehalacha 18 Biurim 7; See previous footnote that the main suspicion is the squeezing of the hair which is applicable in all cases.
Other opinions: Some Poskim write that the custom to avoid bathing in cold water does not apply to an enclosed area, as only one of the worries are applicable, nevertheless he concludes that one may not be lenient unless he is doing so for the sake of a Mitzvah [Tevila] or if one is in great pain. [Ketzos Hashulchan 133 footnote 8; See there that he brings the Beis Yosef as a proof for his statement unlike the M”A ibid who brings the Beis Yosef]
 Conclusion of all Poskim mentioned in Q&A that only permit doing so in a case of a very hot day; Mishneh Sachir 69; Poskim in Piskeiy Teshuvos 326 footnote 112; See Igros Moshe 4/74 and 75 that the Poskim do not discuss this issue and one can infer from Admur and Michaber 326/4 that showering is allowed and seemingly the custom in previous times was to allow showering, however in today’s times the custom has become to prohibit even showering on Shabbos; See Shabbos Kehalacha 18 footnote 91
 Ketzos Hashulchan 133 footnote 8 [towards end]; Igros Moshe 4/74; Beir Moshe 6/73; Dvar Yehoshua 2/54; Az Nidbaru 1/61; SSH”K 14/1; Piskeiy Teshuvos 326/8; Shabbos Kehalacha 18/40; Minchas Yitzchak 6/32 implies that one may not bathe in cold water even to cool off, and may only do so for the sake of a Mitzvah, such as to use a Mikveh, however he then concludes by bringing the Ketzos Hashulchan ibid which is lenient.
 As explained above in Halacha 1 that warm water has the same status as cold water. See above Halacha 1 Q&A there regarding the definition of warm water.
 The reason: Being that in any event from the letter of the law it is allowed, and it is only a custom to be stringent, and in a case of pain this stringency need not be kept. [Poskim ibid]