Mountie is a shortened word for Royal Canadian Mounted Police. And yes they still exist. They are our national police force here in Canada.
They were the first police force to be established in Canada and were originally named "North West Mounted Police" and later changed to "Royal Canadian Mounted Police" They do still do ride horses and mostly for show. And tour the country with their horses and put on a show called the Musical Ride. They do tours to the United States. Recommend that you see them should they ever come to your area.
We do have Provincial Police forces in some provinces and are much the same as your state police forces in your country.
the mounties are a police force that still exists
they were formed to patrol the far away places in Canada where there was little access