Generally if a camera is left at below zero in my experience the battery at the time will significantly reduce in life. However it would normally return to normal after being at room temperature for a while.
I would recommend leaving it without the battery in for a day or so in a warm room and then try again. If the camera charger is a charger that plugs into the camera you could try it without the battery in to test. If not then this is not possible to test.
Potentially there could have been moisture inside the camera at the time it went below freezing and the contraction of the ice against internal components could have caused some damage. I hope this isn't the case for you so I would try drying it out to see if, after a couple of days it springs back to life. It happens more than you might think! I lived in a ski resort for a year and this is common!
All the best, let me know how you get on.
Paul