§ 31-b. State fair. It shall be the duty of the department to hold a state fair to be known as the New York state fair at such times as it may deem proper, and between January first and February fifteenth in each calendar year to publish the time for holding said fair in such year. If such fair be held on the first Monday of September, known as labor day, the department shall designate such day as "organized labor day." It shall not be lawful for any corporation, association or individual to hold or conduct any trotting or pacing race or races during the week in which the New York state fair is held, except upon half-mile tracks, and except at the fairs held by agricultural societies which have received moneys from the state, and no corporation, association or individual holding such races during said week shall be entitled to any of the benefits conferred by article twenty of the membership corporations law, or by any general or special law. The department may make, alter, suspend or repeal needed rules relating to such fair, including the times and duration thereof, the terms and conditions of entries and admissions, exhibits, sale of privileges, payments of premiums, and any other matters which it may deem proper in connection with such fair. It shall furnish to each person who, on the seventeenth day of January, nineteen hundred, was a life member of the state agricultural society, a free admission to the fair ground during the fair of each year during the life of such member.