Information on "Capt. Cook's Co., Mississippi Horse Artillery" appears to be scarce, so the more information you can provide, the better. Civil War Soldiers & Sailors System seems to confirm only one Pat Enright fought for the Confederacy. Pat Enright was in [Greenville] Cook's company. But, Cook (also) was a lieutenant in battery F (Bradford's battery) of the First Mississippi Light Artillery, which may suggest that these "two" units are actually but one with alternate names. I hope others with greater knowledge of the Mississippi artillery units will help with this.