I only use cart to transport wood from my forest, if I'm building something bigger. if the mountain is close to the water, it can be used to drop more silver down and reload it onto the ship,
if I need copper, I pick the one along the shore, pushing your way through the forest with a cart is slow/anoying, and you will load a lot less on cart. On boat you can be overloaded so even a raft may be a better option.