I'd like to represent them in court. DMV laws do not apply to horse & buggy drivers.
Mate, it appears that you have confused the laws of another country with those of your country or State. In Canada (the UK, Australia, NZ, etc...) it is the Highway Act (or variations of the same) and pertains to
a vehicle and the use of public roads. The vehicle does not specifically require a combustion "motor" for propulsion. In the case/story of the OP the vehicle was a buggy utilising a horse for propulsion, being driven in an erratic way. IOW the driver was not completely in control of his vehicle on a public road... the same law would apply to a bicycle, billy-cart or (perhaps) even roller skates if he was causing a danger to others/himself/property.
The driver and passengers where also charged with
Provincial liquor law violations.
"The buggy driver, a 23 year old resident of the Township of Perth East has been charged with "careless driving" contrary to the
Highway Traffic Act. The driver and the two male passengers in their early twenties were also charged with "having liquor in other than licensed premises, residence or private place" contrary to the Liquor Licence Act.
The latter charge
probably means that they had open containers whilst the vehicle was in operation.
In short, you would lose the case for your clients.