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.
Answer
"The capacity of the battery is affected when the temperature drops"
That is incorrect, it is not the capacity (amount of energy stored) that gets lower at lower temperatures. It is the internal resistance of the battery which increases and this lowers the current capability of the lead-acid battery. So you will be able to draw less current (and power) from the battery at low temperatures. The amount of energy stored does not change.
If a lead-acid car battery is in good condition it will still be able to start a car even under cold conditions. A workaround could also be to turn on the lights of the car before starting, now a current will flow warming up the battery and increasing it's current capability. Of course you should only do this when you are sure that the battery has enough stored energy.
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