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Have a cold? Try a minipoo. (1948)
(thelemmy.club)
This brand still existed into the 1970's, advertising under the same name! I assume in the 1940's, the modern slang was not in common use. Some word origin sites say "poo" arose in the 1950's. By the 1970's, this branding must have become problematic!
Nothing wrong with the product, as far as I know. Similar dry shampoos can be purchased today, under rather different branding.
Sounds like a good guess to me. I bet it's something like that.
I guess feeling cold doesn't directly make you catch a cold, but it can stress your immune system, which weakens your defenses vs the virus. Maybe they had similar ideas about wet hair. Nevermind that you'd already have the virus when using the minipoo in the ad's scenario, heh.