This was copied from my friend, Chuck TenBrink's website;
www.cwartillery.org/artillery. Pretty good description of the duties of the Teamsters.

PRIVATES (Teamsters or Wagoneers)
Were under the direction of the QM sergeant and were assigned to drive and care for the baggage wagons (normally two), forage wagons, and sometimes an ambulance. Most of these men were paid an extra rate equal to that of a corporal's pay. These men were considered important not just because they looked after the baggage, but they guarded it with zeal from other troops and commands. Forage and corn for the horses were a much sought after commodity - sometimes by starving infantrymen. Under their care were the wagon teams of either two or four animals, usually mules, and their harness. On the march they were in rear of the battery and sometimes in rear of the army in the baggage train. Also, these men and the extras handled and cared for the extra horses belonging to the battery. Normally a battery would have from four to eight men detailed to this duty; sometimes it was rotated, but often not. Often the teamsters were detailed to the battalion or brigade quartermaster, especially in the later part of the conflict. Many times these men were railed as shirkers from the fighting part of the army. In part this was true, but they performed a valuable service and most did their duty to the end, and even though they did not relish front line positions, they contributed.