What is the freezing point of sulfuric battery acid?
The general effect you're talking about is freezing point depression, one of the basic colligative properties. There are several flavors of lead-acid batteries, so there are different additives that can modulate the freezing point.  The actual composition of the electrolyte varies with the charge state of the battery, so that means the freezing point also varies with how charged it is. I think all of the lead-acid batteries use water as a diluent (it will always be present as it's a species in the electrochemical equilibrium.) From the Wikipedia article on "lead-acid battery": 


  Due to the freezing-point depression of the electrolyte, as the battery discharges and the concentration of sulfuric acid decreases, the electrolyte is more likely to freeze during winter weather.