Are we allowed to take showers on a Three day Yom Tov?
Firstly, the allowances given here to showering on Yom Tov is only when the following conditions are met: a) One will assure not to run into the problem of סחיטה (squeezing) by their wet hair. That is to be careful from squeezing one’s hair from the washing till the drying. Therefore putting a soap or shampoo on the hair may not be done. b) There is no allowance to use bar soaps since that is considered Me’machek (see Mishna Berurah 326:30). c) No fire can be lit or activated by turning on the shower faucet, therefore if the boiler was lit before Yom Tov that should help. However every case needs to be individually checked how the hot water system works in the shower.
Cold water shower on Yom Tov –
It is permissible to take a cold water shower when fulfilling the conditions mentioned above when a person is in great pain. See Shulchan Aruch Orach Chayim 326:1 & Alter Rebbe Shulchan Aruch ibid. Alter Rebbe (ibid:6) concludes that it is the custom not to wash (bath in the outdoor lakes) even in cold water even when there is no prohibition attached to it. The Aruch Hashulchan (326:9) writes on this, “one who breaks this safeguard imposed by the Rishonim [custom of refraining from bathing in rivers, lakes and ponds] , on him it says ‘one who breaks the fence should be bitten by a snake’…”
With that said, the Shemiras Shabbos Kehilchasa 14:11 (source is from Hagaos R. Akiva Eiger 326) brings that a person in pain may have a cold wash, the reasons is since if it is not in a lake, rather just a shower there are less concerns in Halacha.
One should not do this in a public setting like a mikvah. (People might not understand or think that one can also freely use hot water as well.) See Shulchan Aruch Orach Chayim 511:2.
Hot water shower on Yom Tov –
The Alter Rebbe (Shulchan Aruch Orach Chayim 511:1) after bringing a more lenient view, concludes that the custom follows like the view (Rema 511:2) that forbids one to wash his whole body in hot water that was heated on Yom Tov. This is since washing every day is not שוה לכל נפש (necessary for every person) and adds that even if it was heated before Yom Tov we still are to forbid the washing of the whole body by way of decree.
Today it is regular to shower daily, so some Poskim are lenient in extenuating circumstances (where cold water for some reason is not able to clean them) see Mishna Berurah (511:18) allows hot water even if it was heated on Yom Tov. However, as mentioned, the Alter Rebbe does not allow this. Therefore one can wash limb by limb in warm water. when the water is heated before Yom Tov. One should turn on the faucet to wash the face, hands and feet, and can keep the water on to continue washing the rest of the limbs. See Alter Rebbe ibid in the parenthesis.
Little children –
As mentioned, the Alter Rebbe seems to be stringent (by way of custom even with little children who sometimes do not bathe every day), therefore it is best to wash a child limb by limb as mentioned above. If this is not possible, it seems that in extenuating circumstances for example the child could get bad rashes, one can rely on the Mishna Berurah (511:18) who allows to wash a child in hot water on Yom Tov. This would be if it is not possible to wash the little child limb by limb. The water would need to be heated before Yom Tov.