There is no way to stop white frost in the books. Ciri or her children could have a power to open the gates to other world to move all the people to other worlds. Aen Elle can transfer to other worlds a limited amount of people, but Ciri or her children would be more powerful to move all living to another place. The white frost is nothing but an Ice Age, inevidable and theoretically far away in time, so there is no rush, everyone that wanted Ciri to reproduce just wanted to control her genome, to obtain this power and have it under control.
In the games it is hard to explain logically. I think they wanted frost to became a magic anomaly, that consumes the worlds one by one, and thys, should be stopped. I am not shure how she stopped it, as I imagined, she just like, fought the snow or watewer? It was never shown.