The capacity of the battery is affected when the temperature drops, particularly Lead-acid batteries. So how in cold countries this situation is solved.

In this PDF about automotive batteries at low temperature, they have mentioned the specific gravity of the electrolyte is affected when the temperature dips proportionaly the charge as well. This also observed from the graph.

And also is there is any possibility, I have load of 2 amps apart from starter will it function when the battery capacity is reduced to certain low percentage(eg. 50%) at the time of temperature drops.