I like the idea of the combat horse. If the horse earned a fracton of your experience points while you were mounted, it could learn to add to the combat, increasing your land speed, defence, and melee. Could it also jump enemies, fences and baracades? It would be a terrible shame if it got killed though. What about horse armour?
I don't think the cart is necessary as long as you have the teleport stones.
I agree that the animal statuettes should have more of a use. But by that same token, they should be harded to get. You should only be able to receive each one in one of two places in the game, like the castle invitation. Once you earn the statuette, you can attempt the quest you require it for.