This one looks like a school bag and probably dates from the US theatrical re-release in 1958. It's mentioned, along with a "utility bag", in the '58 Snow White pressbook (p.7). Retail price $2.59.
Bag images via escape59.
All players in turn move the same pieces around the board by the spin of the indicators. The winner is the one who is fortunate enough to make the move which releases Snow White from her long sleep by the kiss of the Prince.