The unit started toward Ft Smith, but was called to Fort Gibson in the Indian Territory, where they participated in a running fight with the Indians. In March 1862 they were at the Battle of Elkhorn Tavern or Pea Ridge as people from the north call it. Going toward Shiloh, they were dismounted to fight as Infantry. Their horses were sent home to Texas. They were not in time to fight at Shiloh, but were at the retreat from Corinth and near the Battle of Iuka, MS.
Their first major combat was at Corinth on October 3rd and 4th, 1862. They were charging a fixed artillery site called Robinett. It was well protected but the 9th and 6th Texas almost breached the site when they were overcome with heat, lack of ammunition, men and water. A Union counter attack drove them back. The next morning their commander, General Van Dorn called for retreat. The 9th was beginning to cross the Hatchie Bridge when a Union attack started. The 9th took cover and provided support for 4 units trying to get back across the bridge. The 9th took some killed and wounded but not like the other units. They did help stop the Union and save the day.
In December the unit got their horses back and they participated in the Holly Springs Raid. This action stopped General Grant's march to Vicksburg and delayed the War for several months.
The 9th was now part of General Whitfield's Texas Cavalry Brigade with the 3rd, 6th and 27th Texas Cavalry Regiments. These units would fight together for the rest of the war. In Jan 1863 they went to Tennessee and fought at the Battle of Thompson's Station an captured a Union Regiment.. This was their first battle along side General Forrest. The were part of demonstrations at Franklin and Nashville, before going back to Mississippi.
In Mississippi, they fought skirmishes with Union units of General Sherman. They harassed and delayed. This continued until December 1863 when General Sul Ross took Command. He began to install renewed hope and courage. By May they were again a great fighting machine. The were assigned to the left flank of General Johnston's Army to try and stop General Sherman's march to Atlanta. For over 110 days they fought superior forces, helping to kill over 35,000 Union soldiers at a great cost. As you say, Your Enoch Murphy survived, but he was not through. In July and August od 1864 he helped stop two Union Raids around Atlanta and then went with General Hood's Army to Tennessee again with General Forrest, leading the way in and providing rear guard on the way out. Luckily, they were not used in direct assault at Franklin and Nashville. By the time they returned to Mississippi they were down to the size of two companies. Men had been killed, wounded, left behind sick and become discouraged and gone home. At the end Your Enoch was paroled at Jackson, MS on 15 May 1865. He said his address was Ladonia, TX.
Some of this was taken from Stephen Kirk's book "One Thousand Men of the 9th Texas Cavalry" and some from my web site below. Go and see all they did. Also read Griscom's diary, which is hard to find or Martha Crabb's "All afire to Fight, the Untold Tale of the Civil War's Ninth Texas Cavalry."
You can obtain his military records at this site if you like, an feel free to ask questions.