Deere & Company began producing lawn tractors in 1963 in Horicon, Wisconsin. Like most companies and products, each unit comes equipped with a serial number which can be used to track a specific tractor's model and production year.
The John Deere tractor company places plates on the tractors that will give you the year. If you cannot find it you'll need to contact the company to figure it out. You can find more info at: www.deere.com