I don't recall seeing carts in any silver quest. The quests I can think of which involve silver are:
The French Pirate in the Tavern: the one you've just been doing, no visible way of transporting silver;
The Silver Train: takes place on Petit Tabac, there are some donkeys and crates at the location of the final battle;
Silver for Cartagena: takes place around Cartagena, there are some donkeys carrying crates which appear at the location of the first battle, move to the location of the second battle, then disappear.
The reason donkeys don't appear at all on one quest, appear and stay there in one quest, appear and disappear in one quest, is that the three were written by different authors. "The French Pirate in the Tavern" is the oldest and may even be in the original, unmodded game. "The Silver Train" is a newer quest and different versions of it appear in a couple of storylines. "Silver for Cartagena" is the newest.
The French Pirate in the Tavern: the one you've just been doing, no visible way of transporting silver;
The Silver Train: takes place on Petit Tabac, there are some donkeys and crates at the location of the final battle;
Silver for Cartagena: takes place around Cartagena, there are some donkeys carrying crates which appear at the location of the first battle, move to the location of the second battle, then disappear.
The reason donkeys don't appear at all on one quest, appear and stay there in one quest, appear and disappear in one quest, is that the three were written by different authors. "The French Pirate in the Tavern" is the oldest and may even be in the original, unmodded game. "The Silver Train" is a newer quest and different versions of it appear in a couple of storylines. "Silver for Cartagena" is the newest.