"Supply Wagons would be pulled by horses, mules, donkeys or bullocks, depending upon the era and availability of mounts. Generally each military unit would be assigned wagon or wagons, who would move between the supply train and the unit. Commanders of course would have their own personal wagons, to carry their armor, weaponry, private food stash, treasure and special friend who kept them company during the long nights on campaign."
Since Supply Wagons cannot attack and are defenseless, use Arquebusiers or Halberdiers to defend them and cover them from enemies and defenses.
Supply Wagons only heal the closest damaged troop. If you want them to heal a troop that is badly damaged and distances away, try to recall your troops to a safe spot so your Supply Wagons can heal it.
The A.I. of Supply Wagons are usually one of the strangest. In some moments on the battlefield, Supply Wagons would run into open fields to get shot at and stay there for 0.3 seconds but would later retreat to start healing troops. This has not been patched by Big Huge Games.
Supply Wagons and Wall Sappers are the only troops trained in the barracks that cannot be donated to other players.