I may be misreading, but... logically you can't use the carpet and the horse in the move, if that's also part of the puzzle. That makes no sense.
This is an example of the quirks that come up that are basicly unsolveable. If we throw in logic, everything gets turned upside down.
If you say you cant use the horses and carpet at the same time beacsue its not logical, then when you use a flying carpet, why would you be able to take any of your follower with you at all? they all cant ride the carpet at the same time.
And this kinda stuff is all over the game. What about the pack of horses and the warhorse? if you use the pack for your move and you have a battle, do you get to use the warhorse?
Now you might as well, throw in the old "if its on the mule does it cout?" argument.
Now we have to have item slots, cuz you cant have two pieces of footwear on at the same time. it just goes on and on.