Using the example of a Paladin's mount from the Find Steed spell (as it has the most clarification). If the Paladin is on the mount he controls it and it can take the dash, dodge, or disengage action and moves the Paladin around. If the Paladin isn't on the mount the mount acts independently and can attack.
If the Paladin is in a chariot dragged behind the mount, is he considered on the mount (so that it moves him around the field and can only dash, dodge, disengage) or off the mount (so that it acts independently and can attack) and just happens to also move him around?
I'd think he'd be considered off and the mount would act independently, as I'd also consider him off for the Mounted Combat feat and not allow that to apply.
Best Answer
The mounted combat rules only apply when you are mounted
Here's the introductory text for the mounted combat rules:
The rules specify how you can become mounted:
So these rules only apply when you are mounted on a creature, via the mechanism provided - i.e. you pull yourself onto it and sit on it. Not when you are standing on a chariot a creature is pulling.
This also means the Mounted Combatant feat would not apply:
You get no benefits from this feat while not mounted.
The vehicle rules are minimal
The vehicle rules only specify how much an animal can pull:
And that they have special proficiencies:
These rules do not specify precisely how combat on a chariot would work - so you will have to talk to your DM or make a ruling if you are the DM.
How I would rule
Personally, I would rule this situation as follows:
The mount dragging the chariot acts independently (and thus its actions are not restricted). A normal mount may do things the Paladin does not want - but this is mostly mitigated in this case by the bond specified by the Find Steed spell.
A chariot will have reins - the Paladin can hold these in one or both hands to control the mount and the chariot (restricting its actions as if he were controlling it while mounted). He might want to use these if he had a non-Find Steed mount, or if he wanted to control the chariot through a difficult area. I would probably give disadvantage to any ability checks to control the mount or the chariot if he held the reins one handed.
Side note: do my rulings make chariot use strictly inferior to mounted combat?
There are several reasons why you might use a chariot rather than ride a horse.