They are big, long streetcars pulled by draft horses, not buggy rides. They just go from Town Square and up to the castle and back. They only run in the mornings and early afternoon (they're put away at least an hour before parade time).
It is also a one way trip. So if you have a stroller you have to go back to the other end to claim it..
When we were there in JAnuary the horse actually pooped and we waited to see how long it took someone to come and 'clean up'. It was about 10 minutes.. So unlike disney. I thought the horses had catch bags...