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As we all know, the freezing point of absolute sulfuric acid is 10 °C. The average lead-acid battery (sulfuric) uses ~30% sulfuric acid, and has a freezing point much lower than 10 °C.
What constituents contribute to this effect? What is the diluent used in these batteries? What would the freezing point be?
Batteries have water-sulfuric acid solutions.
There freezing point of water-sulfuric acid solutions varies as a function of concentration in an unusually complex way, having plural local minima and maxima.
This is because the solid has eight identified phases:
$\ce{H2O}$
$\ce{H2SO4 * 6 H2O}$
$\ce{H2SO4 * 4 H2O}$
$\ce{H2SO4* 3 H2O}$
$\ce{H2SO4 * 2 H2O}$
$\ce{H2SO4 * H2O}$
$\ce{H2SO4}$
$\ce{H2S2O7}$
with mixtures of the various phases reaching local minimum freezing points at eutectic points.
The freezing point can be as low as -71 °C near 31% (on an $\ce{SO3}$ basis) and as high as 35 °C near 90%.
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.
What constituents contribute to this effect?
This phenomenon in general is called "Freezing-point depression", and is the process in which adding a solute to a solvent decreases the freezing point of the solvent. It can all manner of solutions. The freezing point depression depends solely on the concentration of solute particles, not on their individual identities, and is thus called a colligative property.
Now, why does this happen? The presence of a solute results in the lowering of chemical potential of solvent; since the lowering occurs even in ideal solutions where enthalpy of mixing is zero (and also since it doesn't depend on the properties of the solute) one can probably guess that it is an entropic effect.
A rough qualitative argument can be made as follows:
We know that liquids possess greater entropy than solids, thus when we freeze something we are going from a "high entropy state" to a "low entropy state". The presence of a solute makes an additional contribution to the entropy of the liquid, and thus this enhanced molecular randomness opposes the tendency to freeze, and consequently we need a lower temperature to freeze.
As an aside, a similar discussion can be applied to the elevation of boiling points of solutions (compared to pure solvents)
What is the diluent used in these batteries?
Typically, it is plain old water
What would the freezing point be?
This is perhaps the most difficult question to answer. If one were to do such a calculation, there are least three complications I can think of.
First, most chemistry textbooks give a simple relation to calculate the depression of freezing point, namely $\Delta T_f = ik_fb$, however, this simple empirical relation just holds for dilute solutions. A more complicated treatment is necessary to deal with concentrated, non-ideal solutions.
The second problem is that the concentration of the electrolyte itself changes during the charge-discharge cycle.
And finally, as @DavePhD has pointed out, the freezing point of water-sulfuric acid mixtures doesn't follow a simple trend.
