The second-broadest category under Minnesota law (definitions, ch, 169) is "motor vehicle", defined in its entirety:
(a) "Motor vehicle" means every vehicle which is self-propelled and
every vehicle which is propelled by electric power obtained from
overhead trolley wires.
(b) Motor vehicle does not include an electric-assisted bicycle, an
electric personal assistive mobility device, or a vehicle moved solely
by human power.
Numerous sub-types of "motor vehicle" or "vehicle" are defined in that section, such as "Class 1 electric-assisted bicycle",
"Farm tractor", "Motorized foot scooter", "Semitrailer" and so on. There is no more-specific category that includes animal-drawn carts of any kind. In Minnesota v. Hershberger, 444 N.W.2d 282 we learn that there must be a religious accommodation made with respect to the slow-moving vehicle statute, insofar as the law requires slow-moving vehicles to have garish warning signs that conflict with Amish religious beliefs. I set aside the possibility that you are referring to a Hindu ceremony re-enacting the Battle of Kurukshetra (millions of chariots).
The first question is whether a chariot is a "slow-moving vehicle". This is set by the characteristic that it is "designed for operation at a speed of 30 miles per hour or less". This is a question of fact and not law, and opinions on the matter differ, however it is more likely than not that a chariot is not designed to travel faster that 30 mph (the internet generally indicates that the physical speed limitation of a chariot is somewhere around 30 mph). Still, even as a slow-moving vehicle, all that is required is "a triangular slow-moving vehicle emblem". Since there is no statutory distinction between a "cart" and a "chariot", there is no legal basis for treating them differently. The concept of "road-legal" is a consequence of other specific classifications. For example, an ATV is regulated under §169.045, but that section does not apply to every vehicle. Since there is no special law addressing animal-drawn carts, they are not specifically prohibited therefore they are "road-legal". §169.045 does allow for local restrictions, therefor you would also have to investigate the specific municipality.