Shiloh and Corinth are good examples of the use of field and heavy artillery.
At the battle of Shiloh McAllister's Battery "D", 1st Illinois Light Artillery operated with four 24-pounder howitzers. These were later considered too heavy for field use; it was not necessarily the weight of the barrel (about 1,300 lbs), but also the logistics of keeping limbers filled. These were the largest field batteries used in the battle on either side.
Also at Shiloh was Madison's Battery "B" 2nd Illinois Light Artillery. They had been designated to serve as siege artillery for the upcoming advance on Corinth, MS. On the morning of April 6 they had five 24-pounder siege guns and an 8-inch siege howitzer. The 24-pounder guns were extremely heavy (3,350 lb barrel) and were pulled by up to ten yoke of oxen (20 oxen). The guns were man handled to the top of the bluff and served as a nucleus for a line of artillery at the end of the first day. As for their 8-inch siege howitzer, it was taken out on to the field on April 7th and served as a field gun...firing 64 pound projectiles!
The Siege of Corinth (April 29-May 30, 1862) included the a battalion of the 1st U.S. Infantry who were also designated as siege artillery. Regular infantry serving as heavy artillery! They had six 30-pounder Parrot rifles, three 8-inch siege howitzers and two 12-pounder Wiard rifles. On the 28th of May the 1st Infantry fired three rounds from one of the 30-pounders which hit on target at the rail crossing 2 1/2 miles away. These were their first shots fired with the weapons. As for field artillery, between the five armies engaged there were 108 field batteries. The Confederates had a small number of siege weapons to defend the city, the largest being a 24lb rifle.
During the battle of Corinth (Oct. 3-4,1862) the 1st Infantry manned three of the seven forts circling the city. The union heavy artillery included eight 30lb Parrots, four 8" siege howitzers, and eight 24lb siege guns. One of the forts (Battery Robinett) had three 20lb Parrotts but these could be found out on the field as well.
There was no horse artillery used during these actions.
Tom