I am not from India but I do know that in many parts of the world Christians do not celebrate 25th December as birth day of Jesus. In fact, when it comes to fundamental Christians (by that i mean people who truly know about Christianity and follow in black and white) they disregard Christmas as a pagan culture adopted by church in 6th century AD just to infiltrate the popular pagan culture. At that time, pagan rituals were to worship sun god with offerings that happened during the mid winter festival starting from 21st December and ending 1st January. Pope Julius 1 decided that as the church was not getting anywhere with the masses so giving birth day to Jesus and celebrating on a specific date would not stand out and would not be so much foreign with the people who would not let go their old habits of pagan rituals and celebrations. Hence 25th December. But many people around the world (I am refering to Christian community) do not belive and celebrate on other days.
What about santa? Well is is an extension of Chris Kringle, the famous personality who was famous for delivering gifts to poor people during the same time of the year and later became saint. His pet dog became the popular reindeers.