At this point in my Scotch... voyage, I find that I know very little about peat and smoke. What I DO know is that I crave it (Laphroaig and Ardbeg: once great enemies of mine; now great friends)! I actually miss my sensitivity to the peat though.
Early on, when there was smokiness, I just assumed it was peat. Later, I discovered they are two distinctly different aromas/tastes (yet not mutually exclusive from one another). Worse yet, there are many discernible types of peat and smoke. All the while my peat sensitivity is being flushed down the toilet.
I believe it is still possible to tune one's peat and smoke senses, but not without education. If I ever learn, I'll be sure to share.