Which 1937 Disney film was the first full-length cel-animated feature?

Answer

Earlier animated features existed, but this was the first in cel animation.

Context

Cel animation draws each frame's moving parts on transparent celluloid sheets, which are laid over a painted background and photographed one frame at a time. Snow White used this on a huge scale, with Technicolor and Disney's multiplane camera, which placed layers of artwork at different distances to give depth. The Library of Congress catalogues the film under that multiplane Technicolor description. The film was released in December 1937, and the studio's investment was large for the time, with a reported cost in the region of 1.5 million dollars, a figure that should be treated as approximate.

The phrase first feature needs the qualifier cel-animated. Britannica says Snow White was the first feature-length animated film and that earlier animation was short, such as J. Stuart Blackton's Humorous Phases of Funny Faces in 1906. Film historians, however, usually point to earlier animated features made with other methods, including Argentina's El Apóstol (1917), now lost, and Lotte Reiniger's silhouette film The Adventures of Prince Achmed (1926).

The Smithsonian's National Museum of American History holds production cels and drawings from the film, which show how finished characters were inked and painted on celluloid.

So the claim holds if read narrowly: the first full-length feature built from cel animation to be widely released, not the first feature-length animated film of any kind.