From my reading of the PHB, chariots are considered 'mounts' for combat and use the same rules.
(A zombie-carried palanquin seems to meet the intent of a chariot, thus a mount).
Cover; no (its just a 'really big saddle')
Higher ground; yes (as long as your target is smaller than your mount!)
Smell; varies based on the mould, fungi and level of decomposition of the zombies.
Stinking cloud; by the rules you would still be affected as the cloud touches the 'squares' you occupy. Levitating 4 zombies and the palanquin would be required first.
However, the problem with levitate is 'one creature or object'. A chariot (or palanquin) is technically 5 separate creatures/objects, so would fail as a group.
Possible get around it by levitating the palanquin and leaving the zombies on the ground to wait for your return.
Stinking cloud is a 20'r sphere, so you're going to need quite a bit of height.
One side note; as your zombies are acting as a non-independent 'mount', they only get to use the Dash, Disengage and Dodge actions. With no hands free, getting them to make unarmed attacks (kicking your enemies...) isn't going to do a lot.