Stretching before is ok but not really necessary other than mobility and activity specific.

Really the idea of a warm up is to prepare the body for exercise (increase heart rate, blood flow and warmth into working tissues and psychologically)….

Purpose of the cool down is to return the body to homeostasis / normal (decrease heart rate etc) and allows the opportunity to maintain and improve flexibility through a stretching sequence. To my mind stretching afterwards is more important as it aids recovery and may help alleviate Delayed Onset Muscle Soreness.