Images via wbmbooks.
The doll was listed in the 1938 wholesale catalog for N. Shure Co. of Chicago. Price per dozen: $3.92.
Catalog scan via gdawg.
During this time period, there were other companies releasing molded hair Snow White dolls. Ideal made one with a composition head and limbs, but it had a stuffed cloth torso. Their company imprint is found on the back of the neck.
Knickerbocker also produced one (left) that is often mistaken for our mystery doll (right).
Knickerbocker image via 15th Blue Book Dolls & Values by Jan Foulke, p.288.
We see that the Knickerbocker company imprint is found on the underside of the back of the head. And the head is a separate piece from the torso.
Our mystery doll, however, has no company imprint. Plus, the head and torso are all one piece.
If you have information on who manufactured this doll, let us know and we'll add your info to this post.
Additional pics via bellusvanitas + debandgen.