October to March is neither a hot season nor a chill season in Andaman. They are dry, so you get to see lot of nature. It's an ideal time to visit Andaman.
Of course between Oct and March, if you are looking for a budget tour, plan during the period between Dushera and Diwali (Oct) which is generally lean season for hotels so they offer at cheaper rate, plan in advance to book cheaper flights.
Between September to March ..if you want to visit Jolly Buoy island for sighting amazing coral reefs and absolutely clean white beach. This island is open from September to March.