It took me a while, since I work almost exclusively with Missouri Civil War history, but I think I found the fight mentioned in the 1889 Goodspeed history of Fulton Co., AR. One of your clues, that it took place in March 1863, was not correct, but your clue that it took place in a swamp near Salem, AR helped me ferret it out of the available record.
Before I go further, the "Clayton" mentioned in Goodspeed is probably Lieutenant Colonel Powell Clayton of 5th Kansas Cavalry Regiment, who was active in southwest Missouri in the spring of 1862.
It appears to me that the battle on Simmons farm may have been the great swamp fight of 12-13 March 1862 between LTC Samuel N. Wood's companies of 6th Missouri Cavalry and Major William G. Drake and several companies of 3rd Iowa Cavalry (about 250 troopers altogether) and a force of several hundred Confederates led by Colonel William O. Coleman, Colonel Archibald McFarland, and Captain J. Posey Woodside. My sources include "Official Records" series 1, vol. 8, pp. 336-9; Dr. W.H.H. Barker's memoirs of being in the 3rd Iowa Cav, "My Memories of the Civil War" he wrote in 1926 available at Camp Pope Bookshop; Broadfoot Publishing Company's "Supplement of the Official Records" vol. 35, 6th MO Cav, pp. 186, 204, 234. The Confederates, who may have ridden here after their reverse at the Battle of Elkforn Tavern (the Union side called it "Pea Ridge"), apparently were attempting to best the Missouri troopers who had been based at Salem for a few days. The Federal troopers discovered the nearby Rebels and struck first, pushing back the southern pickets through the Rebel camps near Spring River Mill until the Confederate force forted up inside a nearby swamp. The Union cavalry attempted to dislodge the Rebels from the swamp with the aid of some cannon, but ran short of ammo after a while and retired back to Missouri, wary that an additional 250 Rebels in the area may approach. The sources I listed state the Union casualties were 4 KIA, 18 WIA, 1 MIA while the Rebel forces may have lost as many as 30 killed, including Captain Woodside. Dr. Barker rode through this battlefield later in the war and found about 30 Rebel graves marked "Killed at Camp Rector." The cannons are a mystery to me, since my records fail to mention artillerymen attached to this Union force, and the Federal army was loath to turn perfectly good artillery ordnance over to cavalrymen to operate. I suppose the cavalry may have operated the fieldpieces anyway.
I hope that helps your quest. I was operating outside of my geographic area, so I was not on solid footing.