Keep in mind the RCMP is not responsible for policing major cities. They are mostly the canadian equivalent of the FBI and also are the provincial police in some (not all) provinces. They also are the local police in small towns.

I've seen mounted policemen in canada, but never a mounted mountie (outside of ceremonial things)

Canada is very big and most RCMP will work along trans-canadian highways. This makes horses unsuited for the job.

AFAIK, they use Dodge Charger Enforcers.

They do have mounted units and RCMP horse carrier trailers.