Mario Kart said:
I would go one step further and plant shady trees on the sideline so the sun does not beat down on the players at all. Forget the fans and mist because the sun's UV rays are still hitting the players which will cause skin cancer later in life. With trees on the sidelines this will protect the players today and in the future. Plus, this is more green for the environment because fans and mist machines use electricity and trees do not.
You need to consider the total environmental impact, though. Trees require water which would require watering, which would use power and water from the municipality which is undoubtedly using high capacity wells which are lowering the water table of the region, and likely not returning water to the same aquifer from whence it was taken, so I think your plan is short sighted to say the least and probably harming the environment, and also if there were winds it would prove a hazard to the players due to limbs which might break off, fall, or be blown on to the playing surface and possibly hitting players, and as the limbs are longer than wide, they could easily penetrate through a face mask and cause serious eye injuries. All in all, from both an environmental and eye care standpoint, your plan is flawed.