Joe,
It makes sense that they were Mississippi rifles. Enfields & Lorenz rifles were also often in the hands of cavalry. Carbines were in rather short supply, and at least the Mississippi rifle was about 8" shorter than standard infantry rifles (although still ~9-10" longer than a carbine.) In the trans-Mississippi, in light of the various fights in the territories and the Mexican War, Mississippi rifles seem to have been rather common at the outbreak of the war. Imports like the Enfield & Lorenz were harder to come by in the theater except through capture.
As an example, during the battle of Wilson's Creek at the beginning of the war, at least some of the soldiers in McCulloch's brigade had Mississippi rifles. One is mentioned explicitly as being used to shoot down Sigel's Capt. Tod who hailed McCulloch. The fellow doing the shooting was a corporal from the Pelican Rifles of the 3rd LA (brigaded with the 1st & 2nd Ark. Mounted, and McRae's Arkansas infantry as well as Greer's South Kansas-Texas Mounted.) At least one other fellow in the 3rd LA is mentioned firing a rifle in this engagement. McCulloch is mentioned by Bearss as carrying a Maynard carbine.
When do you show the 1st Ark Cav receiving those particular weapons? I assume it was before Wilson's Creek. Is this more than one company listed? During the war it was not unusual for various companies of the same regiment to have different arms. This was in fact a pre-war recommendation for various armies--using a few companies equipped as riflemen along with the main body with smoothbores.
Do you happen to have detailed information on the initial arms of the other Arkansas regiments at Wilson's Creek?