I also think it's due largely to cartoons, both Warner Brothers AND Disney, though I think the actual intent was to either add "culture" to kiddie fare or maybe the more pragmatic goal of keeping down production costs. Classical music is public domain so you don't have to pay the fees for creating and using it you would with original score music.
The net effect though is that hearing certain classical pieces is likely to conjure images of Elmer Fudd in a Viking helmet or dancing hippopotami in tutus in the minds of the public at large.