Obviously we are prohibited from any kind of washing on Yom Kippur. Even in Mishnah Yoma it says that a bride may wash her face, implying that the rest of us can't. Yet in temple times, everyone who entered the Beit HaMikdash could not do so without going to the mikvah that day, and the Kohein Gadol immerses himself no less than (I seem to remember) 11 times. How can this be? Is the tradition of not washing ourselves something that only dates to the period after the destruction of the Beit HaMikdash?
I'm really sorry for not answering earlier. I seem to have lost this email.
Immersing oneself for a T'vilas mitzvah is permissible on Yom Kippur. The Shulchan Aruch (613:11&12) explains that nowadays there is no such situation. Had there been such a possibility, it would be permissible. It is for this reason that a Kohen may wash his hands before going up to the Duchan.
A T'vilas Mitzvah constitutes a T'vilah required for something on that specific day, which could have not been done earlier, as is the case with the Kohen serving in the Beis Hamikdash. (He immerses himself five times, and rinses his hands and feet ten times.)
Once again, I'm sorry for the delay.