While a cart is useful for holding containers, which in turn can hold ore, I think it would make sense to have, in effect, a chest on wheels. This could be built using, say, a mixture of cast and wrought iron, and hold somewhat more than a chest. At the moment, roads cannot be built underground, but how about tracks for these carts? Perhaps cast iron could be used to build large-size sections to make it worthwhile.
This would be useful for when mines get very large in size, and it is a long way from the ore to the entrance.