No person shall ride, lead or cause or suffer to be upon park property any horse, pony or mule, except on specifically designated and posted areas or bridle paths. However, Council may grant permits for the holding of horse shows and field trials to recognized civic organizations when, in the judgment of Council, the best interests of the City will be served by such action and provided that an adequate deposit or other arrangement satisfactory to Council is made to ensure a thorough clean-up of the areas used at no additional cost to the City following completion of the event. No person shall fail to complete such clean-up within two days after the conclusion of the permitted event.