Shower with Cold water on Shabbo

Igros Moshe (OC IV 75.1) Question Is it permitted to take a cold shower on Shabbos? Answer I replied previously that we don’t find in the halachic literature the mention that a cold shower is prohibited on Shabbos. Nevertheless it is clear and obvious that most religious Jews on their own initiative do not take cold showers on Shabbos even though they were not told it is prohibited. It is not known if the reason for this this is that this is viewed as abnormal behavior since typically the shower is with warm water. Since there is a prohibition on Shabbos to wash with warm water, even if heated before Shabbos, the whole body. Perhaps because of this prohibition people refrain from cooling off with a cold shower in the summer. Or perhaps it is viewed as a weekday practice. Taken together perhaps these reasons constitute a custom not to take cold showers. However it could also be the result of ignorance and is not a minhag and is thus merely a mistaken practice (minhag ta’os).