1. No known species of reindeer can fly. BUT there are over 300,000 species of living organisms yet to be classified. While most of these are insects and germs, this does not COMPLETELY rule out flying reindeer of which only Santa has seen.
2. There are over 2 billion children (persons under 18) in the world. BUT since Santa doesn't appear to handle Muslim, Hindu, Jewish, Buddhist, etc. children, that reduces the workload down to about 15% of the total (378 million according to the Population Reference Bureau). At an average (census) rate of 3.5 children per household, that comes to 91.8 million homes. One may presume there is at least one good child in each.
3. Assuming he travels east-to-west (which would seem reasonable), Santa has 31 hours of Christmas in which to work, thanks to different time zones and the earth's rotation. This works out to 822.6 visits per second. This means that for each Christian household with good children, Santa has approximately 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 provided, jump back up the chimney, hop back into the sleigh, and move on to the next house.
Assuming each of these 91.8 million households are evenly distributed (which, of course, they are not, but which, for the purposes of our calculations, we will assume to be the case), the average distance between them is 0.78 miles. This results in a total trip of more than 71.6 million miles, not counting stops to (1) do what most of us must do at least once every 31 hours, (2) feed the reindeer, (3) etc. This means Santa's sleigh must move at 640 miles per second (3,000 times the speed of sound). For the purposes of comparison, the fastest man-made vehicle, the Ulysses space probe, moves at a poky 27.4 miles per second. Furthermore, a conventionally-equipped reindeer can run, at best, 15-20 miles per hour.
4. The payload of the sleigh is another interesting factor. Assuming each child gets nothing more than a medium sized Lego set (2 pounds), the fully loaded sleigh is carrying 321,300 tons, not counting Santa, who is invariably described as overweight. On land, conventionally-equipped reindeer can pull no more than 300 pounds each. Even granting that "flying reindeer" (ref item 1) could pull TEN TIMES the normal amount, eight, or even nine (counting Rudolph) reindeer are grossly insufficient to pull the sleigh. In fact, 214,200 reindeer are needed. This increases the gross weight, not counting the weight of the sleigh itself, to 353,430 tons. Again for comparison, this is 4 times the weight of the Queen Elizabeth (the ship not the monarch).
5. 353,000 tons traveling at 650 miles per second creates enormous air resistance, heating up the reindeer in much the same fashion as the space shuttle re-entering 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 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 g-forces 17,500.06 times greater than gravity. A 250-pound Santa (which seems ludicrously slim) would be pinned to the back of his sleigh by 4,315,015 pounds of force crushing his bones and organs resulting in a big pile of worthless pink GOO.
IN CONCLUSION...
If Santa ever DID deliver presents on Christmas Eve, he's dead now.
It seems like you have been doing your homwork! Well, I must confess!: