The thing that is odd is it seemed Snow White would have had everything going in its favor, but since Disney couldn't get the financing, it died in the crib.
Instead, Max Fleischer's Gulliver's Travels became the first animated feature, in 1939, and there we go. Mr. Bug Goes To Town (1941) suffered from being released just before WW2, but Fleischer picked up steam with Puss In Boots (1943), then following up by turning his Superman short cartoons into a full-fledged animated feature in 1945 - a major hit.
Had Snow White hit, Disney had plenty of other ideas (and properties) ready - some movie historians list Pinocchio, Don Quixote and the Tales of Hans Christian Andersen among them - and likely all of them musicals. Hard to see how they'd compete against Fleischer's more sophisticated adventure films as Superman, its sequel Superman Wins the War (1947), and Ali Baba and the Forty Thieves (1950).