So it's no hard work for me, really.

As for the antlers, all animals with antlers shed them (that what's separates them from horns, y'know, though female reindeer (vajor, only shed their antlers once), and the reason is, most probably, as you say, to grow new ones for the next rut. I don't know the specifics when it comes to reindeer, but when you look at their other relatives, such as the red deer or the moose, there you also have a progress in antler size with age, size and also dependant on how good that particular year was, food-wise, and the reindeer shouldn't be an exception.