This question assesses your ability to remain committed under pressure. The address is important and cannot be postponed. This eliminates options (B) and (C), which both suggest stopping or delaying.
Option (A) may not be practical in an urgent setting. The speaker should prioritize the message over minor inconveniences.
Hence, the best course of action is to carry on despite the rain — Option (D). This demonstrates leadership, dedication, and the ability to prioritize purpose over comfort.
\[
\boxed{\text{Continue the address despite the rain}}
\]