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Since my Dad was a U.S.M.C. Officer - we where not allowed to take "Hollywood Showers" (more than 2 minutes total of running water)

So the move to warm to cool to cold shower was no biggie.
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For some reason it is easier to clear the accumulation of lather out of the Mo with warm water, but that may just be my habit.

I clear the lather off of the blade by stropping off on my...

Join the Polar Bear/Cold Water Shaving/James Bond Shower/Dark Side of the Moon....
Never have a problem with the mirror fogging up.

Do use a warm/hot final rinse followed by an ice-water towel......