No. Once and a while is fine- for pure entertainment, but the game is better inside because the ice quality makes the game faster. There are too many natural elements (wind, rain, snow, heat) to depend on with outdoor games.
I think it would be best to keep it indoors so that way they can turn the A/C on and have a cooler environment and not pass out. I used to live in Florida and they had outdoor rinks and that happened to a kid.