There are about 2 billion children (people under 15) in the world. But, since Santa Claus does not appear to handle Muslim, Hindu, Jewish, and Buddhist children, that reduces the workload to 15% of the total - 378 million according to Population Reference Bureau. At an average (census) rate of 3.5 children per household, that's 91.8 million homes. One presumes there's at least one good child in each.
Santa Claus has 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west. This requires him to visit 822.6 houses per second. This is to say that for each Christian household with good children, Santa Claus has 1/1000th of a second to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house.
Assuming that each of these 91.8 million stops are evenly distributed around the earth (just an assumption, of course), we are now talking about 0.78 miles per household, a total trip of 75 million miles, not counting stops to do what most of us must do at least once every 31 hours, plus feeding his reindeers and etc.
This means that Santa Claus' sleigh is moving at 650 miles per second, about 3,000 times the speed of sound. For purposes of comparison, the fastest vehicle on earth, the Ulysses Space Probe, moves at a 27.4 miles per second. Meanwhile, a conventional reindeer can run, tops, 15 miles per hour.
The payload on the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium-sized lego set (2 pounds), the sleigh is carrying 321,300 tons, not counting Santa Claus himself, who is overweight. On land, one conventional reindeer can pull no more than 300 pounds. Even though 'flying reindeer' could pull ten times the normal amount, we cannot do the job with eight, or nine. Thus, we need total 214,200 reindeers. This increases the payload, not even counting the weight of the sleigh itself, to 353,430 tons. That is four times the weight of the great Queen Elizabeth ship.
Imagine 353,000 tons of stuffs traveling at 650 miles per second create enormous air resistance. This will heat the reindeer up in the same fashion as a spacecraft re-entering the earth's atmosphere. The lead pair of reindeer will absorb 14.3 quintillion joules of energy. Per second. Each. In short, they will burst into flame instantaneously, exposing all reindeers behind them, and creating deafening sonic booms in their wake. The entire reindeer team will be vaporized within 4.26 thousandths of a second.
Santa Claus, meanwhile, will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 250-pound Santa Claus would be pinned to the back of his sleigh by 4,315,015 pounds of force! It will Instantly crush his bones and organs and reduce him to a quivering blob of pink goo.
In conclusion. If Santa Claus did exist, he is already dead now.