Well lets think if it is possible:
There are more then 3000.000 living organism that exist on our planet but are not known to our Scientists, most of them are microbs and insects, of course. But there is a chance that flying deer is among them
There are 2billion kids under 18 on this planet. Lets exclude Muslims, Jews, Buddhists and the rest of the non-Catholics....We get about 378million kids which is about 15%from 2billion. According to the UN there are 3.5 kids per family, so we get 91.8million houses to visit. Lets suppose each house has at least one nice kid that deserves a visit from Santa.
Lets suppose Santa begins his working day from the east and moves westward, that makes his working day exactly 31hours. It means he has to visit 822,6 houses per second!! He has only about 1/1000 of a second to visit each house! He has to park his deer, squeeze into the chimney, leave the presents in the socks, eat the cookies, climb out of the chimney...You get the picture.
Lets suppose 91.8million houses he has to visit are spread across the globe evenly (which we know isn't true) that gives us 1.15km between the stops. Whole distance he has to travel is about 113.25 million km. That means he has to travel with the speed about 970km/sec that 3000 times faster the the speed of sound!! (keep in mind that that doesn't include stops to eat or to use the bathroom which you would need at least once in 31hours)
Lets suppose each nice kid gets a lego construction set from Santa which weights abou 1kg. That means his sled must hold 321.300tons of presents (only presents). The standard deer can move only about 150kg of weigh...Lets suppose flying deer a special can move 10 times as much...Will 9 deers be enough? No, we are going to need 214.200 flying dears. That will make the total weight of the sled about 353.430tons
Imagine 353.430 tons moving across the sky with the speed of 970km/sec! The air resistance! First two dears will absorb 14,3KV of energy in a second..Each! They will explode! Well...Whole sled with the deer and Santa will burn in 4,26/1000 of a second. Lets suppose Santa weights 150kg (I know the fatty must weight a lot more) that means that the G-forces will pin him to the seat with the force of 2miilion kilograms!!
well...If he does exist he is already dead!
Father Frost on the other hand does exist and has been very successful in bringing me the gifts every New Year!
I can neither confirm, nor deny above post