Ice houses. It is possible to build houses, usually partially or completely underground, in which snow and ice collected in the winter can be stored, well insulated, well into the summer. read more
It would have been hard to have the ice water on hand since Saladin had been camped out at Hattin for some time and Hattin was quite some distance from Mount Hermon. The battle was also on July 4th so middle of summer, ice wouldn't have lasted long. It's not impossible but I don't think it's likely. read more