Let's face it, a guy who has managed to teach reindeer to fly can probably arrange for them to hold onto their antlers whether or not they have held onto - or ever had - their testicles.
In any case, when Snopes went and asked some rangiferologists at the University of Alaska Fairbanks about antlers, they were told that it is not unknown for a bull* reindeer still to have his antlers at Christmas. More typically they drop off earlier in December, but occasionally they last until January.
* Entire male reindeer are usually called bulls rather than stags. No particular reason, they just are.