Who should pay for water damage bill

[Lee Gierszewski]

Back in early April i received a call from one of my properties claiming that there was water gushing out of the ceiling. I get over there & water is pouring out of the radiant heat system underneath a window. I shut the water off & investigate where the water is coming from. There was an approximate 1 inch split in the 3/4in copper piping. When the plumber came over to fix he stated right away that it was from the water freezing up in the pipe and then splitting the pipe under enormous pressure. Naturally the tenant claims they didn't have the window open. The temperature that night got down to 0 degrees farenheit. I sent the $2000 cleanup bill to the tenant for negligence and she is refusing to pay claiming that my homeowners insurance should cover "old pipes." 

Who do you think should cover this expense?

How should I proceed from here?