The names of the reindeer originated with the 1823 poem "A Visit from St. Nicholas" aka "Twas the Night before Christmas". This solidified the idea of flying reindeer, although if someone has an earlier example, I, too, would like to see it. Rudolph was a late arrival, conceived in 1938 and developed commercially after WWII.

A recent post of mine dealt with the Santa tradition, focusing on the role of Coca Cola, but what was written fits here as well:

Cultural icons like Santa Claus naturally attract a great deal of attention, and anyone who asserts that they found the "real source" of this sort of thing will confront agitated readers and also opponents who will maintain that they, in fact, have uncovered the "real source."

The late twentieth-century American Santa Claus draws on many sources and influences. One of these includes an aggressive Coca-Cola add campaign that helped solidify what the jolly fellow looked like for that time and to the present. Of perhaps even greater importance for the appearance of Santa is Thomas Nast (1840-1902), who presented the nation with his image of Santa during the 1860s.

No single artist created an image in a vacuum, however. Numerous Yule-time supernatural beings (not to mention diverse European traditions about St. Nicholas) can be considered as adding to the current of tradition that flowed forward, giving us what we have today - and each of these entities had an appearance that was more or less agreed upon by believers. Asserting what is the source of Santa is extremely complex, and his image grew out of that evolution. Let's give Coca-Cola its due, but we must understand that its advertisements were nothing more than the latest of many influences that affected the tradition.)