Cabs (including the firewall) were painted inside and out before assembly.

Most generic items like bumpers, inner fenders, etc were also painted before assembly but since theydidn't show, Ford saved the tim eand effort of painteing them individual colors and went withthe black.

Here's an interesting page from the Salesmans Handbook. 1951 Paint specifications, and paint chip chart:

PS These are the late specifications. In late 51 some changes were made. For example in late 1951 all the grills were painted ivory - both regular and "Extra" cabs. The Argent on "Extra" cabs VS body color grille on Standard Cabs scheme used early in 51 was dropped.