In my opinion the lack of horses was probably the reason so many were inside the works and could not excape or were not with their regiment. For example in the Army of Northern Virginia in May 1863 Gen'l Lee's Horse problem was so severe for lack of forage that he literally could not move his reserve artillery from it camps around Fredericksburg. This also limited the ability of Staurt's Cavalry from patroling and guarding the fords west of Fredericksburg. This allowed Gen'l Hooker to steal a two day march on Lee that lead to the Battle of Chancellorsville.

Why would not the condition of Horses been any different in Mississippi? They may have been better foraged because Mississippi has a different growing season than Virginia, but the fact is that cavalry/mounted infantry regiments were always understrength because of this and having good quality Horses for cavalry and artillery was a problem even for the Northern army. Naturally Washington D.C. was one of the norths largest remount depot maintaining a stock of 10,000 horses. The south have far fewer resources for obtaining proper mounts especially after 1862 when the initial supply was depleted.

Remember the old Poem of a British cavalry regiment I believe in the Crimean War "For want of a Nail"?

For want of a nail, the shoe was lost,
For want of a shoe, the horse was lost,
For want of a horse, the rider was lost,
for want of a rider, the squad was lost,
for want of a squad, the Platoon was lost,
......
etc. etc. etc, on and on until the final line was

For want of an army, the War was lost,
All for the want of a nail.

By the way a Horse does its duty every 45 minutes or so. That is the reason why there is so much H.S. in Washington D.C.