If all bodies of water on earth froze and became a gigantic ice skating rink how long before the earth's population would die? Why?

Canadians and Siberians would take over.

We could build igloos on the ice and live on our catches via ice fishing. 

Raw fish anybody? 

I don't know if humanity would become entirely extinct but vast numbers would die in a fairly short time, as would farm animals and crops, and wildlife. No rain to supply the vital water to them. No water, no food, no life.

If there's any comfort in the hypothesis, the Earth did go through something like such a phase in its early history but the cold phases of the latest / present Ice Age simply extended the frigid latitudes. However, a repeat of the last glacial would be extremely disruptive to humanity. At least such events do not happen over-night, and I doubt the next glacial is one to worry anyone alive now! Though those who will be alive then, won't be able to do anything but move to warmer latitudes.