All washing for pleasure is forbidden on Yom Kippur, whether in hot or cold water. No part of the body may be washed, not even the pinky. However, if one was muddied, sullied by excrement, or had a nosebleed, he may wash the affected areas, as his intention is to remove filth, not to derive pleasure. Similarly, after changing a diaper, one may wash one’s hands with soap and water to remove filth and dirt. Even though washing to remove filth involves a small amount of pleasure, since the primary intention is to remove filth, it is not considered washing for pleasure (SA OḤ 613:1).
When preparing food for a child, one may rinse the food or the dishes, as this is not washing for pleasure.
One who is so sweaty that it is really bothering him and causing him to suffer may rinse the sweaty areas, since he is not doing so for pleasure (MB 613:2; SHT ad loc. 4).
One who is very sensitive, and who will be agitated unless he rinses his face in the morning, may rinse his face, though if he is able to refrain, he should be commended. If rheum accumulated in the corner of one’s eyes overnight, and it cannot be removed without water, one may use a bit of water to remove it (Rema 613:4; MB ad loc. 9).
One may not rinse his mouth on Yom Kippur, both because of the prohibition on washing and lest he swallow a drop of water. Even one who knows he has bad breath and is bothered a lot by it may not to rinse his mouth. He may, however, brush his teeth with a dry toothbrush.[2]
If a newlywed bride (within thirty days of marriage) is worried that if she does not wash her face her husband will find her unattractive, she may wash her face; she is not washing for pleasure, but rather to avoid repelling her husband.[3]
One may use a barely damp towel (for example, a towel with which one dried his hands) to wipe his eyes and face, to clean them and refresh himself a bit. This is because the prohibition on washing does not apply something only barely damp. “Barely damp” means that it cannot make something wet enough to wet something else (“tofe’aḥ al menat lehatpi’aḥ”; SA 613:9). As a rule, moist towelettes and baby wipes are too damp and thus may not be used for enjoyment or to refresh. However, they may be used to remove dirt. If they dry out to the point that they are not tofe’aḥ al menat lehatpi’aḥ, one may even use them to refresh oneself.
[3]. This is the opinion of R. Eliezer (Yoma 78b) and the ruling of Rif, Rambam, and Rosh. Some Rishonim (R. Yitzḥak ibn Gi’at and Semag) rule in accordance with the Sages and are stringent. Shulḥan Arukh 613:10 is lenient. Ḥayei Adam 145:15 states that we are not lenient if the groom will not see his bride over the course of Yom Kippur.