As far as I'm aware, Snoopy is a 662 Sqn tradition. Wiley Coyote was acquired during a post-Medicine Man R&R trip south of the border in 1978. One of the pair responsible is a former Guardsman ACM(O) who went on to have a major ginger influence on the Corps.
664 Sqn didn't have a mascot, but following the move from Minden to Dishforth and a change of establishment the whole squadron was taken over by Sumo Flight.