This command did not belong to the state militia. Here are a few lines from my notes on this command, which differ with your statements:

On May 8, 1862, the 10th Alabama Infantry Battalion reorganized under provisions of the Conscript Act, officers and men reenlisting for two years or the war. Two Alabama companies belonging to Martin’s 2nd Confederate Infantry Regiment joined at this time. The Adjutant and Inspector General’s Department designated this new organization the 16th Alabama Infantry Battalion.

John Snodgrass, Jr. Lieutenant Colonel

George L. Alexander Major

John Henry Trippe Surgeon

Leonidas Dixon McReynolds Assistant Surgeon

William S. Stephens Commissary

Absolem Stephen Quartermaster

Benjamin Snodgrass Adjutant

Company “A” of Cherokee County “Cherokee Davis Guards”
Company “B” of Cherokee County “Shorter Guards”
Company “C” of Calhoun County “Oxford Rifles”
Company “D” of Cherokee County “Cherokee Warriors”
Company “E” of Cherokee, Jackson and Marshall Counties
Company “F” of Jackson and Madison Counties “Jackson Hornets”
Company “G” of Madison County “Madison Guards”

Snodgrass’s Battalion was always called the 4th Alabama Infantry Battalion in the field. However, Lieutenant Colonel Snodgrass was advised on October 27, 1862, that another Alabama unit had already received that designation. On February 23, 1863, this organization combined with the 6th Alabama Infantry Battalion to form the 55th Alabama Infantry Regiment.

As far as the company raised by Capt. Snodgrass, the "Jackson Hornets", here is its history:

Recruited near Bellefonte, Alabama, members traveled by rail from Paint Rock Station, Alabama, to Corinth, Mississippi, where they enrolled on June 9, 1861. Captain John Snodgrass, Jr. mustered his command on July 17, 1861. They served as Company “B” of the 2nd Confederate Infantry Regiment (also called the 25th Mississippi Infantry Regiment) until that command disbanded on May 8, 1862. The unit later became Company “D” of the 55th Alabama Infantry Regiment.