Snoop isn't "old school."
"Old School" refers to a distinct period in rap history. It is not a word used to refer to music from an earlier period in someone's career.
"Old School" came into being when "New School" did. There wouldn't have been such a thing as "Old School" unless the "New School" came along and referred to themselves as new school.
Leaders of the New School (featuring a young Busta Rhymes) were just that...the leaders of the "new school." Others were acts such as Young MC, Heavy D, Rob Base and DJ EZ Rock, and to a much lesser extent, Tone Loc. Basically, think any shitty rap music from 1988-93, and that was "new school."
The popularity of "new school" was short lived, as "gangster" quickly took hold. NWA spawned Easy E, Ice Cube and Dr Dre, who in turn spawned Snoop, Nate Dogg and Warren G, (and much later Eminem who spawned D12 and 50 Cent, who spawned G-Unit). Ice T was another prominent gangster rapper, along with MC Eiht, and Too Short, while not gangster, was considered part of that genre.
In the early 90's, when these "new school" groups came out and used the term "new school" to differentiate themselves from "old school" acts such as Run DMC, Slick Rick, Big Daddy Kane and LL Cool J, that is when the term "old school" came into being.
It's a particular genre of music, not a blanket term for anything older than new.
Not trying to be a contrarian, but the misuse of the term "new school" is a peeve of mine.