Algonquin Park used to have a pretty significant equestrian Centre off the Achray road on the East side of the Park (Spoor Lake road I think). They had stables, a head quarters and offered overnight trips with large campsites and troughs for horses. but, I think the operator went out of business in the 80's or 90's.
The park management plan shows interest in expanding activities like horseback riding. In the summers horseback riding is allowed at the Leaf Lake ski trail system, logging roads in the McManus Lake area, and in Clyde and Bruton Townships (when these roads are not being used for logging). Services are provided through commercial operators with specific licenses.
And of course there is the use of horses and horse drawn carts to haul boats, fishermen, camping equipment and fishing gear that is allowed on the road joining the Lake Travers road and White Partridge Lake. Not exactly sure how you would book that.