Here's his palette. Ernest Watson writes, "Note that the colors on the palette's edge follow the color circle of the spectrum—from ultramarine through the blues, greens, yellows and reds to alizarin and rose madder. The colors on the inside row are extra or additional pigments to be used for their particular color identity. The earth group—ochres and siennas—are kept by themselves at the top right of the palette."
In his early career, Carter, like Loomis, Lovell, Rockwell, and other contemporaries, worked within the confines of restricted color palettes. These two-color schemes were usually determined by the magazine, which could only afford black plus one other color of ink. This painting, for instance, would have been printed only in black and yellow, so all the cool colors had to come from grays. This discipline produced great colorists when the magazines made the full printer's palette available later on.
During the period that Carter worked exclusively from life, he would pose the models in a section of the studio where he could black out the ambient light and control the illumination with artificial lights only. However his painting area was under a skylight. Between the two parts of the studio, he drew a black curtain, opened just enough to see the models posing.
One other note: as Stuart Ng mentioned in the comments, Pruett Carter taught at Chouinard Art Institute, where one of his students was Mary Blair, a stylist for the Disney films, herself noted for her bold color designs. There's an exhibit of Mary Blair's work at the Disney Family Museum through September 7 which includes a Pruett Carter original.