[4e] Flying Elven Death Squad

[Edea]

I never said anything about that being a problem, my point was that there are no rules for moving it whatsoever.

By RAW, you can't move the CC at all.

It's probably treating it as a mount like you indicated, so it'd take the move action of the person riding the horse to move (which is why they didn't say "as a move action, you can move the horse and chariot up to 8 squares," as that would only allow the cleric casting it to move it, not the person riding it).
Hell, it conjures "a horse," which pretty much exists in 4e only to be a mount.

The point wasn't that you would leave it on purpose, the point was that one way to effectively pop a CC would be to use powers that Push or Slide enemies off of it, or Grab them and pull them off.

You'd have to spot them first (good luck on that one), THEN get in range, and most likely even if you did those things, the group would force a 1 on you. Dwarven Greaves would also help quite a bit here; most of the other items for the Foot slot stink anyway (though Winged Boots would be preferable).