That was the case with several Texas regiments. There were definitely Texas cavalry regiments on the field at Honey Springs. The Texas cavalry (dismounted) held the center of the Confederate line. I know the 29th, in particular, took heavy losses in the fight. The 29th, 30th and 31st Cavalry regiments fought across much of the Indian Territory and Western Arkansas during the war.
I'll post some of the letters here over the next couple of days as I can transcribe them, since they will probably be of interest to others as well.
I have quite a few photos of the battlefield and the OR reports on my site at www.exploresouthernhistory.com/honeysprings1.