One should wash his face and feet every day out of respect for G-d, as the verse states “For in the image of G-d he created man”. [One who goes to Mikveh in the morning fulfills this mitzvah with the immersion. Some rule that in modern times that people no longer walk barefoot it is not required to wash the feet daily.]
Drying the face: [One must dry his face well after washing as] not drying it well can lead to cracks in his skin or to boils. If one did not do so then his cure is to wash his face many times in water that had beets/spinach [cooked] in it.
Drying the feet: Placing (socks or) shoes on one’s feet which are wet from bathing can lead to blindness r“l. [Therefore one must dry his feet prior to putting on his socks or shoes as is the law regarding all matters which endanger a person. Nevertheless the custom of the world, including Rabbis and other G-d fearing Jews, is not to be particular to dry the feet prior to wearing socks or shoes, and G-d nevertheless protects them from danger. Thus being that this is the custom, and G-d prevents the danger from occurring, one may even do so initially.]
Is one to avoid drying his feet after Mikveh?
It is proper to leave at least one area of one’s body wet from the Mikveh water in order so the body absorbs the holy water. Based on the above one may let his feet remain wet and dry the remainder of his body in order to fulfill this directive.
May one wash his face before drying his hands from the washing water?
Some write that one is to dry his hands from the morning washing water prior to rinsing his face. Alternatively one is to pour a fourth time over his hands and he may then rinse his face. This applies even when one is washing a second time after using the bathroom.
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 Kama 4/21
 Ketzos Hashulchan 2 foot-note 25
 Ketzos Hashulchan 2 footnote 25 in name of Mishneh Berurah 260/4 and Peri Megadim; So is also implied from the footnote in Admur 75/1 on the words “in areas that they walk barefoot” that this washing is only needed to be done in places where people walk barefoot. [Ketzos Hashulchan supplements page 82]
Ruling of Kabalists: The Kabalists write that today there is no need to wash the feet as we are unable to remove the Kelipos from the feet. Only the Kohanim in the Mikdash have ability to do so. [Yafeh Shaah 2; Ben Ish Chaiy Toldos 1; Soles Belula 4/2; Kaf Hachaim 4/5]
 Kama 4/20
 Ketzos Hashulchan 2/10
 Lit. Tradin. This is also called silka as mentioned in Hilchos Rosh Hashana 583. It is defined as either spinach or beets. Vetzaruch Iyun.
 So is implied from Rashi Berachos 39a “Meiy Silka”
 Admur Choshen Mishpat Hilchos Shmiras Haguf Vihanefesh Halacha 9 based on Gemara Pesachim 111b
 Parentheses in original. This teaches us that even socks may not be placed on wet feet.
Other Opinions: There are opinions [Likkutei Mahrich Seder Hanhagos Erev Shabbos] which hold that there is no need to dry the feet prior to placing socks. Furthermore if one places on socks then he may even place his shoes on with his covered wet feet. Nevertheless from Admur ibid which adds socks in parentheses it is understood that the hazard applies even with socks. [Shaareiy Halacha Uminhag 3/13]
 Ketzos Hashulchan 2/10
 Shaareiy Halacha Uminhag 3/13
 Machatzis Hashekel 260; brought in Ketzos Hashulchan 73 footnote 1
 Based on Teshuvah of Tzemach Tzedek, elaborated on in Shaareiy Halacha Uminhag 3/13.
 Shaareiy Halacha Uminhag 1/131
 See Kaf Hachaim 260/5 in name of Arizal that one is to not dry off the Mikvah water on Erev Shabbos. The Rebbe ibid extends this custom as well to the daily immersion.
 Machazik Bracha 4/2; Kaf Hachaim 4/8; See however Piskeiy Teshuvos 4/3
 As also the bathroom contains an impure spirit and hence one is to avoid placing this water on his face. [ibid]