The six officers began the first leg of the Great Horses for Health Relay 2021 at the Wentworth Woodhouse estate, near Rotherham, yesterday.
They will carry a baton on patrol with them until May 6, when they will hand it over to West Yorkshire Police.
It will then be taken on a tour of the UK by other mounted officers, civilian horse riders, carriage drivers, walkers and cyclists this summer.
Horses 4 Health, the charity organising the relay, hopes it will raise £600,000 for equine charities and show people that spending time with horses can improve their mental health.
Sarah McLeod, chief executive of the Wentworth Woodhouse Preservation Trust, said: “We are proud to host the official launch of the first ever Great Horses for Health Relay and see the baton passed from the charity to South Yorkshire Police Mounted Section for the inaugural leg of its journey.
“It’s easy to understand how being around horses can have a positive impact on people’s lives.
“They have always been a big part of the history of this house.”
The baton will be carried around Scotland, Northern Ireland, the Isle of Man, Wales and England before the relay finishes on the South West coast on October 2.