There are approximately two billion children (under 18 years of age) on Earth. However, since Santa does not visit Muslim, Hindu, Jewish or Buddhist children (except maybe in Japan), this reduces the workload for Christmas night to 15% of the total, or 378 million. By counting an average of 3.5 children per household, this amounts to 108 million homes, presuming that each includes at least one good child.
Santa has about 31 hours of labor on the night of Christmas, thanks to the different time zones and the rotation of the earth, assuming he travels east to west, which appears elsewhere logic. This works out to 967.7 visits per second. This means that for each Christian household with at least one good child, Santa has about one thousandth of a second to park the sleigh, hop out, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left for him, get back up the chimney, jump into the sleigh and move on to the next house.
Assuming that each of these 108 million stops are evenly distributed on the surface of the Earth (assuming that we know to be false, of course, but we will accept a first approximation), we must count on about 1.4 miles per house. This means a total trip of more than 150 million miles, not counting stops or pee.
Therefore, Santa's sleigh is moving at 1170 kilometers per second (3000 times the speed of sound). For comparison, the fastest vehicle made by man, the Ulysses space probe, crawls to 49 kilometers per second and an average reindeer can run at its best at 27 miles an hour.
The payload of the sleigh adds another interesting element. Assuming that each child gets nothing more than a box of average Legos (one kilo), the sleigh is carrying over 500 thousand tons, not counting the weight of Santa himself.
On land, a conventional reindeer can pull no more than 150 pounds. Even assuming that the famous "flying reindeer" is ten times better, the job of Santa Claus could never be accomplished with 8 or 9 cattle, he would need about 360 000. This increases the payload, not counting the weight of the sled, to 54 000 tons, roughly 7 times the weight of the Queen Elizabeth (the ship, eh, not the monarch). 600,000 tons traveling at 1170 miles per second creates enormous air resistance.
This would heat up the reindeer in the same manner as a spacecraft re-entering Earth's atmosphere. Both of the reindeers at the head of each convoy absorb heat energy from 14 300 million joules per second. In short, they blaze almost instantaneously, exposing the reindeer behind. The entire reindeer team would be completely vaporized within 4.26 thousandths of seconds, just long enough for Santa to reach the fifth house on his trip.
No big deal anyway, since Santa, who would leave from zero to 1170 km/s in a millisecond, would be subject to accelerations up to 17,500 G's. A Father Christmas of 125 pounds (which seems ludicrously slim) is pinned to the back of the sleigh by a force of 2 157 507,5 pounds, instantly crushing his bones and organs and reducing him to a small pile of pink, quivering flesh. Therefore, if Santa did exist, he's dead now.
Merry Christmas!