They were following orders. Don't try it at home, being elite is a lot of work.
Nazis were generally stupid shits who followed their stupid leader over the cliff.
Since they were not effective at thinking for themselves, someone must have told them to use milk. Belonging to a supreme race requires that you do weird shit with animal emissions.
I don't think it's so much of a Nazi thing as it is a traditional pedicure kind of thing. I used to work/volunteer a lot at a nursing home and a lot of old ladies would talk about it - particularly a mix of milk and honey.