What causes exactly that batteries are slower when temperature drops? When it is getting colder there are less molecules in the air or the molecules are getting slower. 
Now in a battery the chemicals involved don't get less and the electric forces to get the battery work isn't also lessened. So if the surrounding air is getting colder how can this has an effect on the battery?
 A: A battery generates the potential difference by using a type of chemical reaction called a redox reaction. Like all reactions, the redox reactions in a battery are affected by the temperature - more precisely the free energy of the reaction changes with temperature. This changes the potential difference that the reaction produces, and it therefore changes the voltage produced by the battery.
There are some unrelated affects that also make a battery work less well when it's cold. For example the internal resistance increases as the temperature is decreased, so for any given current the voltage drop inside the battery also increases with decreasing temperature.
Danger: tedious details follow!
Suppose we have some reaction that exchanges $z$ electrons and has a Gibbs free energy of reaction $\Delta G$. If the cell potential difference is $E$ then the work is just:
$$\Delta W = -|z|FE $$
where $F$ is Faraday's constant (the charge per mole of electrons). With a bit of hand waving we can equate this work to the change in the gibbs free energy, so we end up with:
$$ \Delta G = -|z|FE $$
and we can rearrange to get the expression for the EMF of the cell:
$$ E = -\frac{\Delta G}{|z|F} \tag{1} $$
So the change in the battery EMF with temperature is due to the change in the Gibbs free energy with temperature.
For a chemical reaction such as the redox reaction in the battery the Gibbs free energy change is related to the enthalpy and entropy change by:
$$ \Delta G = \Delta H - T\Delta S $$
For a spontaneous reaction, such as the one in the battery, $\Delta G$ is negative, and the equation above shows that as we increase the temperature it tends to make $\Delta G$ more negative i.e. the magnitude of $\Delta G$ increases. Conversely decreasing the temperature makes $\Delta G$ less negative i.e. the magnitude of $\Delta G$ decreases. Plugging this result back into equation (1) above we find that the cell voltage increases with increasing temperature and decreases with decreasing temperature.
A: I'm not an expert in the chemistry of batteries, but they are based on a redox chemical reaction, and the rate $r$ of a chemical reaction can be generally described by an Arrhenius or similar law, i.e.
$$r (T) \sim \exp\left(-\frac{E_a}{k_B T}\right)$$
where $E_a>0$ is the activation energy, that is to say the energy that must be supplied to the system in order for the reaction to start.
You can see that $r(T)$ increases with T, and that $r(0)=0$. So, the lower the temperature, the slower the reaction.
A: The kinetics and the internal resistance are the cause of it. They are both temperature dependent. You can see the temperature term in Butler-Volmer equation: https://en.wikipedia.org/wiki/Butler%E2%80%93Volmer_equation that can be used to describe the electrochemical kinetics. 
If it is Li-ion, you have the diffusion of ions from one electrode to another, which is also temperature dependent. They also pass through the electrolyte, whose conductivity is affected by the temperature. The polymer separator can also be affected by the low temperature. It also depends on how low is the temperature and if these terms are really affected. The list can continue. 
I like to think at it like if it would be a chemical reaction. The rate of a reaction is affected by the temperature. You can use Arrhenius equation to give you an idea. The lower the Temperature,  the slower the Reaction. 
