The reindeer who pull Santa's sleigh look nothing at all like the spike white-tail deer in the parade. Reindeer males (reindeer are domesticated caribou) lose their antlers throughout December and early January, females in the summer.

Shucks, I wouldn't waste powder or an arrow on that little bitty critter that was offed by the stoplight. If it WAS full grown it's genetically recessive, as it would have no antlers to speak of with which to engage other males and perpetuate its genes.