The silliness began in the early 1960s, with designs by artist Bill Justice.
Prancing around on television in "Disneyland Around the Seasons", December 1966.
Vintage Paper Models from Disneyland's Entertainment Art Department
Throughout the 60s, 70s, and 80s, the holiday parade changed names a few times (Christmas In Many Lands Parade, Fantasy on Parade, Very Merry Christmas Parade, Disneyland Christmas Fantasy...) but the Silly Reindeer remained their same silly selves.
Disneyland Parade Model from the early 1980s.
In 2003, Santa got himself a brand hew herd. More attractive, perhaps. But 100% un-silly. As blank as a you-know-what in the headlights.
The Silly Reindeer were shouted out with glee in this 1966 issue of Jack and Jill Magazine. Click to Enlarge.