In steeplechases and hurdle races, any horse losing its rider may be remounted by such rider in any part of the same field or enclosure in which the occurrence took place, but should such horse not be caught until it shall have entered another field, then such horse shall be ridden or brought back to the one in which it parted from its rider. Any rider so losing his or her horse may be assisted in catching the horse and remounting it without risk of disqualification.
N.Y. Comp. Codes R. & Regs. Tit. 9 § 4066.1