Rice's battery was not assigned until much later, the date of the order being May 13, 1864.
You may be thinking about the words to the song about Forrest. which mentions "Forrest's artillery battalion; Morton, Rice and Walton and Thrall."
The battery in your other question is Ferrell's Georgia Battery, which served with Roddey's cavalry from December 1862 until the end of the war.
If I'm not mistaken, one of Ferrell's lieutenants later shot Forrest and received a mortal wound for his trouble. Two of Ferrell's guns were captured and disabled during the fighting at Day's Gap AL, Apr. 30, 1863, and Forrest held the lieutenant in charge of this section to blame.