Like the topic says, what happens when a players deck runs out of cards?

Nothing, specifically. You don't lose (like you would in Magic) if you cannot draw... you simply have to make do with the tools you have in play (and in your hand, discard pile, and dead pile).

BenStark said:

cry?

As difficult as it may seem, that wasn't my first thought.

But my opponent had three Frostfang peaks and it was Winter...