You can't upgrade a horse like it is an item like in current mmos. You can most likely give it the top feed and take care of it so it works at it's highest proficiency.
The closest I can see to an "upgrade" in terms of animals is if you breed your horse with a better one, to get stronger offspring.
For the wagons, I'm not sure if we will be able to take parts off and replace them. If we can replace parts on wagons( not just repair current parts) then when crafters get skilled we could upgrade wagons for sure.