One slight problem with your logic...
No known species of reindeer can fly. But there are 300,000 species of living organisms yet to be classified, and while most of these are insects and germs, this does not completely rule out flying reindeer.
There are 2 billion children (people under 10) in the world, but since Santa doesn't (appear) to handle the Muslim, Hindu, Jewish and Buddhist children, that reduces the workload to 15% of the total - 378 million.
At an average 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 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 (which seems logical). This works out to 822.6 visits per second.
This is to say that for each Christian household with good children, Santa 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.
91.8 million stops works out at about 0.78 miles per household, a total trip of 75.5 million miles, not counting stops to do what most of us must do at least once every 31 hours. And to feed the reindeer.
This means that Santa's sleigh is moving at 650 miles per second, 3,000 times the speed of sound. By comparison, the fastest manmade vehicle, the Ulysses space probe, moves at a poky 27.4 miles per second. 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 (1 kilogram), the sleigh is carrying 321,300 tons, not counting Santa, who is himself a little porky.
On land, conventional reindeer can pull no more than 130kg. Even granting that "flying reindeer" could pull ten times the normal amount, we cannot do the job with Santa's eight, or even eight hundred. In fact, we need 214,200 reindeer. This increases the payload - not even counting the weight of the sleigh - to 353,430 tons. This is three times the weight of the Titanic.
353,000 tons traveling at 650 miles per second creates enormous air resistance - this will heat the reindeer up in the same fashion as a spacecraft reentering 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 almost instantaneously, exposing the reindeer 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, meanwhile, will be subjected to around 17,500.09Gs of centrifugal force.
A 100kg Santa (which seems ludicrously slim) would be pinned to the back of his sleigh by 1,957,257kg of force.
In conclusion - If Santa ever did try to deliver presents on Christmas Eve, he's dead now. Sorry!