Lieutenant Colonels
The three colonels in Marlowe's brigade are lieutenant colonels. John Wayne's character is listed as "Colonel John Marlowe" in IMDB, and Willis Bouchey's character is listed as "Colonel Phil Secord". Despite the fact that the third colonel in the brigade has some dialog before turning back, he is not listed in IMDB's credits which include many minor characters not credited in the movie.
It is easy to tell the ranks of characters called colonels in westerns or Civil War movies if you can get a halfway decent look at their shoulder straps. A shoulder strap has a raised border and a background the color of the branch, yellow for the cavalry and emerald green for the medical branch, with the rank insignia on the background. Full colonels have eagles with spread wings, lieutenant colonels have oak leaves, thus the expressions "bird colonel" and "leaf colonel".
And you don't have to be able to recognize the insignia to tell the rank. A colonel's single eagle is placed in the center of the shoulder strap and a lieutenant colonel's two oak leaves are placed at the ends of the shoulder strap. Thus when seen from the front they will both have one insignia showing, but a colonel's eagle will be at the center of the shoulder strap while the lieutenant colonel's oak leaf will be at the front of the shoulder strap.
The last time I saw The Horse Soldiers I checked and Colonel Marlowe clearly had lieutenant colonel insignia. It would be very unusual for colonels to be under the command of a lieutenant colonel, and as well as I could tell Colonel Secord and the other colonel also had lieutenant colonel's insignia.
A regular army cavalry regiment would have five field officers: a colonel, a lieutenant colonel, and three majors. I think that volunteer cavalry regiments in the Civil War had the same number of field officers. At the dinner with Hannah Hunter, the surgeon, Major Kendall, was seated at one end of the table opposite to Hannah Hunter, and Marlowe, Secord, and four other officers were seated at the sides of the table. Assuming that they were all field officers the other four should have been majors.
Thus it seems that the cavalry regiments in Marlowe's raid were missing their colonels and short on majors. And that is not too surprising. A brigade was almost as likely to be commanded by the colonel of one of its regiments as by a brigadier general, but obviously this brigade is not, instead being lead by one of its lieutenant colonels.
Possibly some of the missing colonels and majors are on detached duty at a headquarters, on court martial duty, on leave, being treated for wounds, etc. Or some of them may have left the army through death or resignation, etc. and not yet been replaced.
It is possible that Marlowe is described as a lieutenant colonel in Harold Sinclair's novel that the script is based on. Or maybe John Ford decided to make Marlowe a lieutenant colonel for some reason. Or maybe John Wayne kept as souvenirs the lieutenant colonel's shoulder straps he wore as Kirby York in the epilogue of Fort Apache (1948) and/or as Kirby Yorke in Rio Grande (1950) and wanted to wear them again in The Horse Soldiers (1959)