N.O.S. AG tires or any tire used for low speed applications pose little danger and as long as they weren't stored in direct sunlight and will probably provide a full life expectancy if not cut or torn.
What you must avoid is purchasing out dated tires used for high speed applications, such as automobile, truck & bus, motorcycle etc. These tires can cause fatal accidents when they disintegrate from age at high speeds.
It is very wise to be aware of tire manufacture dates for any tire to be used over the road at highway speeds. Your life can depend on it.