In winter,air over Siberia cools and sinks,causing a high pressure area north of the Himalayas.This in turn creates winds that blow across india and out over the Indian ocean.This wind system is called north-east monsoon which is responsible for most of the rainfall in the state of Tamilnadu in India. 
Monsoons are sudden seasonal reversals in wind direction.They bring heavy rain.India is affected by south-west monsoon(June to September) and north-east monsoon(october to December).During south-west monsoon the entire India,except Tamilnadu gets the rainfall.As Tamilnadu happens to be in the rain-shadow area(Tamilnadu is on the leeward side of the Western ghats mountain range which obstructs the south-west monsoon),there is not appreciable rainfall during this period.On the other hand,it gets rainfall during the north-east monsoon period as the monsoon winds which originate as dry winds ,pick up lot of moisture on its way from the Bay of Bengal and strike the east coast of Tamilnadu(which is the only coastal area on its way along with Srilanka)) causing more rain.Moreover many low pressure systems develop in the Bay of Bengal during this period and move towards the east coast causing heavy rainfall.Some of the systems become cyclone also giving torrential rain and with strong winds.
It is due to retreating monsoon. The retreating monsoon runs from October to November, when the pressure on land slowly increases where as the pressure over the Bay of Bengal falls down.So, the wind start to move from north to south and humidity from the Bay of Bengal and this causes rainfall in Tamilnadu in winter.Tamilnadu gets rainfall at the last because this is in rain shadow region.