An Open Enrollment Period is the time of year when you can enroll in private health insurance. The next open enrollment period will begin on November 1, 2020 and will end on January 31, 2021. The New York State of Health has implemented a COVID-19 Special Enrollment Period for private health insurance through September 15, 2020. Remember, you can enroll in Medicaid, Child Health Plus and the Essential Plan all year round.