Depends upon the severity of the drought. If it's not bad, I doubt antlers ill be affected. In fact, I've seen great antler growth in years with less than average precip. Deer and elk can forage/browse on quality feed even in dry conditions.
Not sure where you are or how bad it is, but the impacts of drought vary quite a bit. It'll affect the breed up and the condition of overwintering fawns a lot next winter, but the bucks seem to grow good antlers the first year of a dry period.