Bathing for a mourner during the thirty days in the days of the Omer

During the days of the Omer, when everyone observes the prohibition of haircuts, is a mourner allowed to bathe in hot water as usual?

The ruling is the same as during the thirty days, and bathing is not permitted due to the Omer.

In explaining the custom not to bathe for thirty days, the Or Zarua wrote that it is due to the concern that one might comb their hair after bathing. (We permit combing as stated in the Shulchan Aruch, Siman 390). The Maharshal wrote that the reason is due to a decree lest one might get a haircut after bathing, as it was their custom to do so. The Taz questioned in SK 1: if so, why is it not forbidden for everyone to bathe during Chol HaMoed, since haircuts are forbidden during the festival, and we might fear that due to bathing, one might get a haircut? The Taz answered that only in mourning, when one person is forbidden to cut hair, do we fear that through bathing, he might come to cut his hair, but during Chol HaMoed, when everyone is forbidden to cut hair, we do not fear that he will cut his hair as he will be reminded of the prohibition. The Pitchei Teshuva in Yoreh Deah, Siman 381, SK 2, wrote: "According to this, it is possible that if the festival of Pesach or Sukkot falls within the seven days, when the decree of thirty days is not annulled, as stated in Siman 399, it is permitted to bathe during Chol HaMoed, as the decree of haircuts does not apply, since it is forbidden due to Chol HaMoed, and in this case, there will be no errors since there is a prohibition for the entire world." Some have written to permit bathing during the days of the Omer for this reason, since everyone is forbidden to cut hair, and the reason of combing does not apply in our times as we are accustomed to combing, but in Tov Taam VeDaas, Part 3, Siman 223, it is written to prove that one should not bathe, and even if the reason is annulled, the custom is not annulled. This is also proven by the opinion of the Mishnah Berurah, as he forbade haircuts during Chol HaMoed in Siman 548, SK 41.