Honestly not sure, but certainly sometime in the 20th century. It was my main e-mail back then, I migrated to Yahoo! shortly after the Microsoft buyout and kept the HoTMaiL as a throwaway. When Google announced Gmail and the 1GB (with projection to infinite) storage I switched to them as soon as I got an invite, but when they changed their slogan from "Don't be evil" to "Do the right thing" with the Alphabet restructure I ditched it and moved to my own domain with Fastmail. If Fastmail starts to show signs of evil it will be as easy as updating my domain records to point toward OurMailIsActuallyGoodIPromiseThisTime.com and click through the certificate warnings on my mail clients.
That Hotmail branding survived long after the purchase; in the last few years it's the same interface as their 365 business offering now, and under outlook.com branding.